Question

Please help me establish the identity of the equation shown. Must show work.

Answer 1

`\begin{gathered} (sec\text{ V+tan V\rparen}^2=\frac{1+sinV}{1-sin\text{ v}} \\ from\text{ the left hand side} \\ ((1)/(cosv)+(sinv)/(cosv))^2 \\ \\ \\ =((1+sinv)/(cosV))^2=((1+sinv)^2)/((1-sin^2v))=((1+sinv)(1+sinv))/((1+sinv)(1-sinv)) \\ \\ Cross\text{ the common factor \lparen1+sinv\rparen} \\ \\ \\ (1+sinv)/(1-sinv) \end{gathered}`