Question

Prove the following identities
(1- sinA - CosA) = 2 ( 1-sinA) (1-cosA)​

Answer 1

Answer:

Actually, the question has some mistake.

The question shuold be:

Prove (1-sinA+cosA)²=2(1-sinA)(1-cosA)

Explanation:

Consider the L.H.S.: 

(1-sinA+cosA)² = [(1-sinA) + cosA]²

=  (1-sinA)² + cos²A + 2(1-sinA)cosA 

=  1 + sin²A − 2sinA + cos²A +2(1-sinA)cosA  

=  1 + (sin²A + cos²A) − 2sinA + 2•(1-sinA)• cosA

=  1 + 1 − 2sinA + 2(1-sinA)cosA    [Since, sin²A + cos²A = 1] 

=  2 − 2sinA + 2(1-sinA)cosA 

=  2(1 − sinA) + 2(1-sinA)cosA 

=  2(1 − sinA)(1 + cosA) 

=  2(1 − sinA)(1 + cosA) 

= R.H.S.

Please mark as brainliest