Question

Prove the following.​

Answer 1

Answer:

Hello!❤️

Step-by-step explanation:

(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

Answer 2

taken theta = @

LHS

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

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

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

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

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

RHS

Hence LHS = RHS

proved

identity used

• (a + B)^2 = a^2 + B^2 + 2aB
• sin^2@ + cos^2@= 1