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Trigonometric Ratios & Identities formula sheet

Every formula in the Trigonometric Ratios & Identities chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 21 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Angles, signs and standard values

Radians and signs
3× asked, last 2026
π rad=180∘,1 rad≈57∘17′,s=rθI: all+,  II: sin⁡,cosec⁡+,  III: tan⁡,cot⁡+,  IV: cos⁡,sec⁡+\begin{aligned}&\pi\ \text{rad}=180^\circ,\qquad 1\ \text{rad}\approx57^\circ17^\prime,\qquad s=r\theta\\&\text{I: all}+,\ \ \text{II: }\sin,\operatorname{cosec}+,\ \ \text{III: }\tan,\cot+,\ \ \text{IV: }\cos,\sec+\end{aligned}
s=rθs=r\theta needs radians. Fix the quadrant before any square root: sin⁡x=−3/5\sin x=-3/5 in III gives cos⁡x=−4/5\cos x=-4/5.
Allied angles
6× asked, last 2025
f(n⋅90∘±θ)=±{f(θ),n evenco-f(θ),n oddf(n\cdot90^\circ\pm\theta)=\pm\begin{cases}f(\theta),&n\text{ even}\\ \text{co-}f(\theta),&n\text{ odd}\end{cases}
Sign: of ff in that quadrant (θ\theta acute). Co-: sin↔cos, tan↔cot, sec↔cosec. cot⁡(90∘+θ)=−tan⁡θ\cot(90^\circ+\theta)=-\tan\theta.
Standard values
8× asked, last 2026
sin⁡15∘=3−122,tan⁡15∘=2−3tan⁡22.5∘=2−1,sin⁡18∘=5−14cos⁡36∘=5+14,sin⁡236∘=5−58\begin{aligned}&\sin15^\circ=\frac{\sqrt3-1}{2\sqrt2},\qquad \tan15^\circ=2-\sqrt3\\&\tan22.5^\circ=\sqrt2-1,\qquad \sin18^\circ=\frac{\sqrt5-1}4\\&\cos36^\circ=\frac{\sqrt5+1}4,\qquad \sin^236^\circ=\frac{5-\sqrt5}8\end{aligned}
cos⁡15∘=(3+1)/22\cos15^\circ=(\sqrt3+1)/2\sqrt2, tan⁡75∘=2+3\tan75^\circ=2+\sqrt3, cos⁡72∘=sin⁡18∘\cos72^\circ=\sin18^\circ, cosec⁡18∘=5+1\operatorname{cosec}18^\circ=\sqrt5+1.

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Practise Trigonometric Ratios & Identities

18 more formulas in 5 topics

Identities and elimination; Compound angles; Multiple and sub-multiple angles; Transformations, products and series; and Maximum and minimum values. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Identities and elimination

  • Pythagorean identities5×
  • a sin⁴θ + b cos⁴θ2×

Compound angles

  • sin and cos of A ± B8×
  • Product of sums and differences
  • tan of sums6×

Multiple and sub-multiple angles

  • Double angle6×
  • Triple angle3×
  • Half angle4×
  • t = tan(θ/2)

Transformations, products and series

  • Sum to product7×
  • Product to sum
  • Sines or cosines in AP
  • Cosine doubling product2×
  • θ, 60° − θ, 60° + θ6×
  • Telescoping5×

Maximum and minimum values

  • a sin θ + b cos θ7×
  • Ranges via one variable6×
  • Bounds and AM–GM4×

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About 85 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

Practise Trigonometric Ratios & Identities

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Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

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