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Sum-to-Product and Product-to-Sum Formulas - Practice Questions & MCQ

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

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In ABC if tanC2(atanA+btanB)=a+b, then the triangle is

Concepts Covered - 1

Sum-to-Product and Product-to-Sum Formulas

Product into Sum/Difference
1. 2cosαcosβ=[cos(αβ)+cos(α+β)]
2. 2sinαsinβ=[cos(αβ)cos(α+β)]
3. 2sinαcosβ=[sin(α+β)+sin(αβ)]
4. 2cosαsinβ=[sin(α+β)sin(αβ)]

Proof:
We can derive the product-to-sum formula from the sum and difference identities.

cosαcosβ+sinαsinβ=cos(αβ)+cosαcosβsinαsinβ=cos(α+β)2cosαcosβ=cos(αβ)+cos(α+β)sin(α+β)=sin(α)cos(β)+cos(α)sin(β)+sin(αβ)=sin(α)cos(β)cos(α)sin(β)+sin(α+β)+sin(αβ)=2sin(α)cos(β)cos(αβ)=cosαcosβ+sinαsinβcos(α+β)=(cosαcosβsinαsinβ)cos(αβ)cos(α+β)=2sinαsinβ

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Sum-to-Product and Product-to-Sum Formulas

Mathematics for Joint Entrance Examination JEE (Advanced) : Trigonometry

Page No. : 3.8

Line : 36

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