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Double Angle Formulas - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Double Angle Formula and Reduction Formula is considered one of the most asked concept.

  • 40 Questions around this concept.

Solve by difficulty

If 6cos2θ+2cos2θ/2+2sin2θ=0,π<θ<π, then θ=

(1+tan22)(1+tan23) equals

If sinα=35, find sin2α and cos2α(0<α<90)

If sinA=3/5, where 0<A<90. Then the value of sin(2A)?

The value of tan3Atan2AtanA is equal to

Concepts Covered - 1

Double Angle Formula and Reduction Formula

Double Angle Formula and Reduction Formula

sin(2θ)=2sinθcosθ=2tanθ1+tan2θcos(2θ)=cos2θsin2θ=12sin2θ=2cos2θ1=1tan2θ1+tan2θtan(2θ)=2tanθ1tan2θ

Proof:

The double-angle formulas are a special case of the sum formulas, where α = β.

For sine

sin(α+β)=sinαcosβ+cosαsinβ
If we let α=β=θ, then we have

sin(θ+θ)=sinθcosθ+cosθsinθsin(2θ)=2sinθcosθ
For cosine

cos(α+β)=cosαcosβsinαsinβ
Letting α=β=θ, we have

cos(θ+θ)=cosθcosθsinθsinθcos(2θ)=cos2θsin2θ

We can write this formula in different forms as per the requirement of the question,

cos(2θ)=cos2θsin2θ=(1sin2θ)sin2θ=12sin2θ
The second variation is:

cos(2θ)=cos2θsin2θ=cos2θ(1cos2θ)=2cos2θ1

For tan
Replacing α=β=θ in the sum formula gives

tan(α+β)=tanα+tanβ1tanαtanβtan(θ+θ)=tanθ+tanθ1tanθtanθtan(2θ)=2tanθ1tan2θ
Reduction Formula
The double-angle formulas can be used to derive the reduction formulas, which are formulas we can use to reduce the power of a given expression involving even powers of sine or cosine.

sin2θ=1cos(2θ)2cos2θ=1+cos(2θ)2tan2θ=1cos(2θ)1+cos(2θ)

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Double Angle Formula and Reduction Formula

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Reference Books

Double Angle Formula and Reduction Formula

Mathematics for Joint Entrance Examination JEE (Advanced) : Trigonometry

Page No. : 3.11

Line : 26

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