Question

Sin theta-cos theta = root2cos then prove that sintheta+costheta=root2sin theta

Answer 1

Please find the answer in the attachment.

Answer 2

Step-by-step explanation:

sinθ - cosθ = √2 cosθ

Squaring both sides,

sin²θ + cos²θ -2sinθcosθ= 2cos²θ

sin²θ - cos²θ = 2sinθcosθ (transposing 2cos²θ to LHS and 2sinθcosθ to RHS)

(sinθ+cosθ)(sinθ-cosθ)=2sinθcosθ (a²-b²=(a+b)*(a-b))

Given sinθ-cosθ=√2cosθ,

√2 cosθ(sinθ+cosθ)=2sinθcosθ

== sinθ+cosθ=√2 sinθ

Hence Proved