Playbook
Trigonometry - I
99 q - 1.85/paper - 37% HARD. Trig Identities, Compound Angle and Equations is 77 of its 99 questions. Weightage has FALLEN (2.20 lifetime to 1.85 recent), the largest decline of any live chapter.
- Questions in the bank
- 99
- q/paper (2024–25 shifts)
- 1.85
- Tagged HARD
- 37%
- Subtopics
- 2
Strand: Long Tail
When you’ll see it
An identity to simplify or prove, a general solution of a trigonometric equation, or a compound-angle expansion.
How this chapter is tested
99 q lifetime — the largest chapter in the long tail by raw count — but only 1.85/paper on recent shifts. That gap is the story: its weightage has FALLEN from 2.20 to 1.85, the largest decline of any live chapter. Preparing from lifetime frequency over-invests here, and the correction is to hold it at the tail's normal budget rather than treating it as a big chapter.
37% HARD, and 77 of the 99 questions sit in a single subtopic (Trig Identities, Compound Angle, and Equations) at 36% — a large and comparatively soft block by long-tail standards, where Limits runs 56% and Trigonometry - II 49%.
The bank files triangle work under two chapter headings: Properties of Triangle here at 22 q, and Properties of Triangles — Sine/Cosine Rules and Projection in Trigonometry - II at 52 q. A drill link to one covers only part of the material, so plan both together.
Beyond its own marks, this chapter is infrastructure. The identities feed trigonometric limits, the substitution and trigonometric-integral work in Indefinite Integration (159 q, 3.35/paper, 51% HARD), and the polar form in Complex Numbers. Weak identities are felt three chapters away, which is why it stays on the plan even as its own weightage falls.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
The identity toolkit
Pythagorean, reciprocal and quotient identities, plus the standard values at 0, 30, 45, 60 and 90 degrees. Everything downstream assumes these are instant.
Compound angles
sin(A plus or minus B), cos(A plus or minus B), tan(A plus or minus B). Note that cosine flips the sign: cos(A + B) = cos A cos B - sin A sin B.
Multiple and half angles
The double-angle forms, the three expressions for cos 2A, the half-angle substitutions, and sum-to-product and product-to-sum conversions. Choosing the right one of the three cos 2A forms is usually what makes an expression collapse.
General solutions
sin x = sin a gives x = n pi + (-1)^n a; cos x = cos a gives x = 2 n pi plus or minus a; tan x = tan a gives x = n pi + a. Learn which family each equation belongs to before solving.
Triangle relations
Sine, cosine and projection rules, shared with Trigonometry - II. Same content, second home.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Principal solution offered for a general one
The question asks for the general solution and the distractor gives the principal value, or the reverse. Read the demand before solving.
Roots lost by dividing
Cancelling a common trigonometric factor discards every root that makes that factor zero. Factorise and set each factor to zero instead — the option with fewer roots is the planted one.
Cosine compound-angle sign
cos(A + B) carries a minus and cos(A - B) a plus, which is the opposite of the sine formulas. The sign-swapped option is standard.
Extraneous roots from squaring
Squaring both sides to remove a surd or a mixed expression introduces roots that do not satisfy the original equation. Every root must be substituted back.
Drill every trigonometry - i question
99 questions from the bank, scoped to 2 bundled subtopics.
Drill one subtopic at a time
The 2 subtopics this playbook covers, in catalog order.
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