Question

prove that( cosec theta- cot theta )^2= 1- cos theta / 1+ cos theta

Answer 1

Step-by-step explanation:

(cosec x-cot x)^2 = (1-cos x ) / (1+cos x)

[(1/sin x) - (cos x/sin x)]^2 = [2.(sin (x/2))^2] / [2.(cos (x/2))^2]

((1-cos x) / sin x)^2 = [tan(x/2)]^2

{[2.(sin (x/2))^2]/[2.sin(x/2).cos (x/2)]}^2 = [tan(x/2)]^2

[sin(x/2) / cos(x/2) ]^2 = [tan(x/2)]^2

[tan(x/2)]^2 = [tan(x/2)]^2

LHS = RHS

hence proved

Answer 2

Answer:

Step-by-step explanation: