Question

1. If = (cos + sin ), show that 1 + + 2 = (1 + 2 cos )(cos + sin ).

Answer 1

Step-by-step explanation:

Given,

cosθ+sinθ=

2

cosθ

squaring on both the sides, we get,

cos

2

θ+sin

2

θ+2sinθcosθ=2cos

2

θ

cos

2

θ−sin

2

θ=2cosθsinθ

(cosθ+sinθ)(cosθ−sinθ)=2cosθsinθ

2

cosθ(cosθ−sinθ)=2cosθsinθ [ Given cosθ+sinθ=

2

cosθ]

∴cosθ−sinθ=

2

sinθ [henceproved]