Question

please prove that and give solution​

Answer 1

Answer:

cos(90-theta)/1+ sin(90-theta)

+ 1+sin(90-theta)/cos(90-theta) = 2cosec theta

LHS

= sin theta/( 1+ cos theta) + (1+cos theta)/sin theta

take lcm add them

we get

= (sin²theta + (1+cos theta)²)/((1+costheta).sin theta)

= ( sin²theta + 1 + cos²theta + 2 costheta)

divided by ((1+costheta).sin theta)

=( 1+1+2cos theta)/((1+costheta).sin theta)

= 2(1+cos theta)/(1+cos theta).sin theta

= 2/sin theta

= 2cosec theta

LHS = RHS

hence proved

hope this will help you