Question

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

Answer 1

Answer:

Step-by-step explanation:

Consider the LHS:

(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) = RHS

Hence Proved !!!!