Question

Question 5 (iv)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
(iv) $\frac{(1+secA)}{secA}=\frac{si{n}^{2}A}{(1-cosA)}$
[Hint : Simplify L.H.S and R.H.S separately]

Answer 1

$\left(iv\right)\frac{(1+secA)}{secA}=\frac{si{n}^{2}A}{(1-cosA)}L.H.S.=\frac{(1+secA)}{secA}=\frac{(1+\frac{1}{cosA)}}{\frac{1}{cosA}}=\frac{\frac{(cosA+1)}{cosA}}{\frac{1}{cosA}}=cosA+1R.H.S.=\frac{si{n}^{2}A}{(1-cosA)}=\frac{(1-co{s}^{2}A)}{(1-cosA)}=\frac{(1-cosA)(1+cosA)}{(1-cosA)}=cosA+1L.H.S.=R.H.S.$