Trigonometry Questions for SSC CHSL

Standard Angle Values Table

This table is the backbone of all direct value questions. Learn it cold. The angles tested are 0, 30, 45, 60, and 90 degrees. SSC CHSL often puts the answer directly from this table, or uses it as a step inside a bigger expression.

• sin 0=0, sin 30=1/2, sin 45=1/root2, sin 60=root3/2, sin 90=1
• cos values are sin values in REVERSE order: cos 0=1, cos 30=root3/2, cos 45=1/root2, cos 60=1/2, cos 90=0
• tan = sin/cos: tan 0=0, tan 30=1/root3, tan 45=1, tan 60=root3, tan 90=undefined
• cosec, sec, cot are just reciprocals of sin, cos, tan respectively
• sin^2(45)+cos^2(45) = 1/2 + 1/2 = 1 — always verify with Pythagorean identity

Pythagorean and Core Identities

These three identity groups appear in simplification questions almost every exam. SSC CHSL loves to give a messy trig expression that collapses neatly once you apply the right identity. Practice recognizing the pattern quickly.

• sin^2(A) + cos^2(A) = 1 — most used identity
• 1 + tan^2(A) = sec^2(A), so sec^2 - tan^2 = 1
• 1 + cot^2(A) = cosec^2(A), so cosec^2 - cot^2 = 1
• These also give: sec^2 - tan^2 = (sec+tan)(sec-tan) = 1, useful for finding sec+tan when sec-tan is given
• If sin+cos = k, then squaring gives sin^2+cos^2+2sincos = k^2, so 2sincos = k^2-1

Complementary Angle Identities

SSC CHSL frequently asks questions where one angle is the complement of another, meaning they add up to 90 degrees. The trick: sin of an angle equals cos of its complement. Same for tan-cot and sec-cosec pairs. These questions look tricky but solve in seconds once you know the rule.

• sin(90-A) = cosA, cos(90-A) = sinA
• tan(90-A) = cotA, cot(90-A) = tanA
• sec(90-A) = cosecA, cosec(90-A) = secA
• Classic SSC pattern: sin(27) x cosec(63) — since 27+63=90, cosec(63)=cosec(90-27)=sec27, so expression becomes sin27 x sec27 = sin27/cos27 = tan27
• Any pair of trig functions summing to 90 will cancel or simplify beautifully

Height and Distance

These are word problems involving angles of elevation or depression. A person looks up at a tower — that angle is elevation. Looks down from a cliff — that is depression. SSC CHSL usually tests simple one-step problems using tan formula. Two-building or shadow problems appear occasionally.

• Angle of elevation: tan(angle) = height / horizontal distance
• Angle of depression from top = angle of elevation from bottom (alternate angles) — common trap
• tan30 = 1/root3, tan45 = 1, tan60 = root3 — these three cover 90% of H&D problems
• If angle is 45, height = horizontal distance — no calculation needed
• Shadow problems: tan(sun angle) = object height / shadow length

Important Trig Expressions and PYQ Shortcuts

SSC CHSL loves a specific set of expression types that repeat across years. Knowing these patterns saves precious time. These are not random — they follow a few templates.

• sinA.cosecA = 1, cosA.secA = 1, tanA.cotA = 1 — always equals 1
• sin^4A - cos^4A = (sin^2A - cos^2A)(sin^2A + cos^2A) = sin^2A - cos^2A
• (sinA + cosA)^2 = 1 + 2sinAcosA and (sinA - cosA)^2 = 1 - 2sinAcosA
• If tanA + cotA = k, then tan^2A + cot^2A = k^2 - 2
• sin^6A + cos^6A = 1 - 3sin^2Acos^2A — this formula appears in SSC papers directly

• Confusing sin(90-A)=cosA with sin(90+A)=cosA — the second is wrong. Only subtraction gives this rule for complementary angles.
• In height-distance problems, using sine or cosine instead of tangent when opposite and adjacent sides are given — always check which two sides you have before picking the ratio.
• Forgetting that angle of depression from top equals angle of elevation from bottom — many students draw wrong diagrams and use wrong angle.
• Calculating root3/2 as 0.75 instead of approximately 0.866 — this causes wrong answer in MCQ matching. Know exact values, not decimals.
• Squaring sin+cos=k and forgetting the 2sincos cross term — they write sin^2+cos^2=k^2 and get 1=k^2, losing the key information.

• Sin table trick — ALL SILVER TEA CUPS: values under root for sin are 0,1,2,3,4 divided by 4 for angles 0,30,45,60,90. Cos is the reverse.
• For Pythagorean identities remember 1 STEP UP: sin-cos stays 1, then tan-sec and cot-cosec both add 1 to give the square of the other.
• SOHCAHTOA for right triangle basics: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
• Complementary shortcut — FLIP THE NAME: sin flips to cos, tan flips to cot, sec flips to cosec when angle changes to 90-A.

• SSC CHSL typically gives 2 to 3 trig questions — one is usually a direct table value substitution, one is an identity simplification, and one may be height-and-distance. Do table values first as they take under 30 seconds.
• Expressions involving sec-tan or cosec-cot almost always use the shortcut (sec+tan)(sec-tan)=1. Spot this pattern instantly.
• Height-distance problems in CHSL stay at 30, 45, or 60 degree angles only. You will never see a random angle like 37 degrees — so memorize only those three tan values.
• If a question has complementary angle pairs like sin(A).cosec(90-A), recognize that cosec(90-A)=secA, then it becomes sinA.secA = tanA. These solve in 10 seconds.
• Avoid expanding everything algebraically in trig simplifications — first check if Pythagorean identity collapses the whole expression in one step. CHSL setters design questions for that shortcut.