SSC CGL Trigonometry Questions 2026 — Free Chapter Wise Practice Test

Trigonometry Tests — Pick a Level and Start

Tap a level to see every test in it. Level 1 is set at real SSC CGL difficulty — start there the day you finish the identities. Level 2 is pitched above the exam, to push accuracy under pressure.

Trigonometry looks like a long formula list and behaves like a short one. Almost every question in the SSC CGL paper is an algebraic identity wearing trigonometric clothes: a difference of squares, a perfect square, a sum of cubes, or a quantity added to its own reciprocal. Once you see which algebraic shape is in front of you, the trigonometry is only the last line.

Three facts carry most of the chapter. sin² θ + cos² θ = 1 and its two cousins turn every squared expression into something smaller. Complementary angles swap the ratio for its co-ratio, which is why sin 21° and cos 69° are the same number and why long products of tangents collapse to 1. And the conjugate pairs — sec θ ± tan θ, cosec θ ± cot θ — multiply to 1, so knowing one member hands you the other. Each test puts twenty-five questions in front of you in one sitting, which is what turns those three into reflexes.

How Many Trigonometry Questions Are Asked in SSC CGL?

Trigonometry is one of the reliable scoring blocks of advanced maths. Counting height and distance separately, it is worth two to three questions in Tier I and three to four in Tier II Paper I — and the identity questions among them are usually the quickest marks on the page.

Counts vary by shift. Trigonometry, geometry and mensuration together make up the advanced-maths half of the paper, and trigonometry is the one that rewards memorised identities most directly.

What You Will Practice in the Trigonometry Chapter

Ratios, identities and angles

• One ratio given and another asked, through the right triangle and the Pythagorean triples 3-4-5, 5-12-13, 8-15-17, 7-24-25 and 9-40-41
• A ratio with the quadrant named — getting the sign right before the value
• Expressions built from the standard angles 0°, 30°, 45°, 60° and 90°, with coefficients and squares
• Complementary angles: sin(90° − θ) = cos θ, tangent products that collapse to 1, and squared pairs that add to 1
• Allied angles and reduction of large or negative angles — 1230°, −870°, 600° — to the first turn
• Homogeneous fractions in sine and cosine, cleared by dividing through by cos θ (or cos² θ)
• Identities to simplify, and identities to recognise among four options
• Conjugate pairs sec θ ± tan θ and cosec θ ± cot θ, split, squared and inverted
• sin θ ± cos θ and sin θ cos θ converted into each other, and into cubes
• Power sums: sin⁴ θ + cos⁴ θ = 1 − 2p and sin⁶ θ + cos⁶ θ = 1 − 3p
• A ratio plus its reciprocal, squared and cubed — tan θ + cot θ, sin θ + cosec θ
• Conditions that force a single angle, such as sin θ + cos θ = √2 or sin θ cos θ = ½

Angles, ranges and figures

• Maximum and minimum of a sin θ + b cos θ, of weighted squares, and AM–GM bounds with the equality point checked
• Trigonometric equations solved for an acute angle, including quadratics with a root to reject
• Compound angles: sin(A ± B), cos(A ± B), tan(A ± B), and exact values such as 15°, 75° and 22½°
• Double, triple and half angles, run forwards and backwards
• Sum-to-product and product-to-sum, and chained products such as cos 20° cos 40° cos 80°
• Elimination of the angle from a pair of expressions — the ellipse and hyperbola forms
• Ratios of the angles of a triangle, where A + B + C = 180°
• Radian and degree measure, complements and supplements, arcs and sector areas
• Where a ratio is undefined, which values are impossible, and how many angles satisfy a condition

Rules worth memorising

The first three rows answer the majority of Tier I trigonometry questions on their own. The power-sum row is the one that turns a frightening sixth-power expression into a single subtraction.

The three mistakes that cost the most marks

• Reading the sign off the ratio instead of the quadrant. A sine of ½ is not enough to place an angle — 30° and 150° share it. Fix the quadrant first, then the value; in the third quadrant a negative sine and a negative cosine give a positive tangent.
• Stopping one step short. Squared answers are the commonest wrong tick: tan² θ = 2 is not the tangent, and sin²(θ÷2) = ⅛ is not the sine. Read whether the question wants the square, the root, or the reciprocal.
• Using AM–GM without checking the equality point. sec² θ + 4cos² θ really does bottom out at 4, but 4cosec² θ + sin² θ never reaches the bound of 4 the same argument suggests, because it would need sin² θ = 2. When the equality point is out of range, the minimum sits at an endpoint instead.

Solved Examples — SSC CGL Trigonometry Questions

How the Trigonometry Chapter Tests Work

• 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
• Optional 15-minute timer — with the clock to build exam speed, without it while you are still learning the identities.
• Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
• Solutions, shortcut tricks and concept notes open after you submit, question by question.
• English and हिंदी, chosen at the start of every test.
• Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.

How to Prepare Trigonometry for SSC CGL

1. Learn the standard-angle table cold. 0°, 30°, 45°, 60° and 90° for all six ratios, written from memory in under a minute. Everything else in the chapter assumes it.
2. Name the algebraic shape first. Before touching an identity, ask whether you are looking at a difference of squares, a perfect square, a sum of cubes, or a quantity plus its reciprocal. The trigonometry is the last line, not the first.
3. Keep the three Pythagorean identities in both directions. You need 1 − sin²θ = cos²θ as often as the forward form, and tan²θ − sec²θ = −1 catches people out.
4. Turn every conjugate pair into its partner immediately. Given sec θ + tan θ, write the reciprocal underneath before doing anything else.
5. Reduce p first. When fourth or sixth powers appear, find p = sin²θcos²θ and both answers follow without ever finding the angle.
6. Divide homogeneous fractions through. Every term carrying exactly one sine or cosine means dividing by cos θ leaves only tangents; if every term is a square, divide by cos² θ.
7. Fix the quadrant before the value. Write down which ratios are positive there, then read the size off the reference angle.
8. Check what is actually asked. Square or root, ratio or reciprocal, θ or 2θ — most wrong options are the correct working stopped one step early.
9. Do Level 1 untimed, the same day you finish the identities. It is set at real SSC CGL difficulty; the aim is picking the right identity, not speed.
10. Repeat Level 1 with the 15-minute clock on, then move to Level 2. After that, verify against a previous year paper and a full mock test under locked sectional timing.

Related SSC CGL Maths Chapters

Trigonometry sits on algebra and feeds the advanced-maths block. Practising these together is the fastest route through that half of the paper.

All SSC CGL Chapter Wise Tests

Every chapter below has its own free Level 1 and Level 2 tests with full solutions.

SSC CGL Trigonometry Questions — Frequently Asked Questions

More Free SSC CGL Practice