Question

Prove that : (1-sin theta+cos theta)2= 2 (1+ cos theta) (1-sin theta)

Answer 1

Answer: I'm writing theta as @...

Properties used: 1.sin@=2sin(@/2)cos(@/2)

2.cos@=2cos^2(@/2)-1

SOLUTION:

(1-sin@+cos@)^2=(2cos^2(@/2)-2sin(@/2)cos(@/2))^2=

4cos^2(@/2)(cos(@/2)-sin(@/2))^2=

2(2cos^2(@/2))(1-2sin(@/2)cos(@/2))=

2(1+cos@)(1-sin@)

Hence,Proved...

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