Question

Prove (1+sina+cosa)²=2(1+sina)(1+cosa)

Answer 1

Step-by-step explanation:

{(1+Sina) + Cosa}²

(1+Sina)² + Cos²a + 2(1+Sina)(Cosa)

1 + Sin²a + 2Sina + Cos²a + 2Cosa(1+Sina)

2 + 2Sina + 2Cosa(1+Sina)

2(1+Sina) + 2(1+Sina)Cosa

2(1+Sina)(1+Cosa)

Answer 2

Answer:

$lhs= ( {1 + \sin( \alpha ) + \cos( \alpha ) })^{2} \\ 1 + { \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} + 2 \sin( \alpha ) + 2 \sin( \alpha ) \cos( \alpha ) + 2 \cos( \alpha ) \\ 1 + 1 + 2 \sin( \alpha ) + 2 \sin( \alpha ) \cos( \alpha ) + 2 \cos( \alpha ) \\ 2 + 2 \sin( \alpha ) + 2 \sin( \alpha ) \cos( \alpha ) + 2 \cos( \alpha ) \\ 2(1 + \sin( \alpha ) + \sin( \alpha ) \cos( \alpha ) + \cos( \alpha ) \\ 2(1 + \sin( \alpha ) )(1 + \cos( \alpha ) )$

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