Question

(1 - sine A+cos A)square = 2 (1+coseA)
(1-sinA)​

Answer 1

Answer:

LHS = (1-sinA+cosA)²

= [(1-sinA) + cosA]²

= (1-sinA)² + cos²A + 2(1-sinA)cos A

= 1 + sin²A − 2sinA + cos²A + 2(1-sin A)cos A

= 1 + (sin²A + cos²A) − 2sinA + 2(1-sinA)cos A

= 1 + 1 − 2sinA + 2(1-sinA)cosA

[Since, sin²A + cos²A =1]

= 2 − 2sinA + 2(1-sinA)cosA

= 2(1 − sinA) + 2(1-sinA)cos A

= 2(1 − sinA)(1 + cosA)

= RHS