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sohit badhwar

· started a discussion

· 1 Months ago

Ques 53 (Question:1096395.0)

How cosB .cos(alpha) becomes (sin alpha .sinB-cos alpha.cos B)

Question:

     If  α+β-γ=π   , then  sin2α+sin2β-sin2γ   = ? 

Options:
A)

  2sinα.sinβ.cosγ   

B)

  2cosα.cosβ.cosγ   

C)

  2sinα.sinβ.sinγ   

D)

  2cossα.cosβ.sinγ   

Solution:

α+β=π+γ   

then,  sin(α+β)=sin(π+γ)   

then,  sinα.cosβ+cosα.sinβ=-sinγ   

squaring both sides

⇒sin2α1-sin2β+sin2β1-sin2α+2sinα⋅cosβ⋅cosα.sinβ=sin2γ   

⇒sin2α-sin2α.sin2β+sin2β-sin2α.sin2β+2sinα.cosβ.cosα.sinβ=sin2γ   

⇒sin2α+sin2β-sin2γ=2sinα.sinβ(sinα.sinβ-cosα.cosβ)   

=  -2sinα.sinβ.cos(α+β)   

=  -2sinα.sinβ.cos(π+γ)   

=  2sinα.sinβ.cosγ   

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