Show that 1/(1+cos(90° – θ))+ 1/ (1 – cos(90° – θ)) = 2 cosec^2 (90° – θ)

Question

Show that \(\frac{1}{1+cos(90° -θ)}+\frac1{1-cos(90° – θ)}\) = 2 cosec² (90° – θ)

Answer 1

L.H.S. = \(\frac1{1+sin\,θ}+ \frac1{1-sin\,\theta}\) = \(\frac{1-sin\,\theta+1+sin\,\theta}{(1+sin\,\theta)(1-sin\,\theta)}\)

= \(\frac2{1-sin^2\,θ}= \frac2{cos^2\,\theta}\) = 2sec² θ

R.H.S.= 2 cosec² (90° – θ) = 2 sec² θ. 

∴ L.H.S. = R.H.S