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If α + β + γ = π, then the value of sin2α + sin2β – sin2γ is equal to

(a) 2 sin α 

(b) 2 sin α cos β sin γ 

(c) 2 sin α sin β cos γ 

(d) 2 sin α sin β sin γ

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(c) 2 sin α sin β cos γ

sin2 α + sin2 β – sin2 γ 

= sin2 α + sin (β + γ) sin (β – γ)       [Using sin2 A – sin2 B = sin (A + B) sin (A – B)] 

= sin2 α + sin (π – α) sin (β – γ)        ( α + β + γ = π) 

= sin2 α + sinα sin (β – γ)                  ( sin (180º – θ) = sinθ) 

= sin α [sin α + sin (β – γ)] 

= sin α [sin (π – (β + γ) + sin (β – γ)] 

= sin α [sin (β + γ) + sin (β – γ)] 

= sin α [sin β cos γ + cos β sin γ + sin β cos γ – cos β sin γ] 

           ( sin (A + B) = sin A cos B + cos A sin B) 

= 2 sin α sin β cos γ.

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