Question

Please verify my answer. I am not sure if it is correct.

Answer 1

now, we're making the assumption we're simply doing an identity proof, so

`sec(\theta )-tan(\theta )sin(\theta )=\cfrac{1}{sec(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE 1st step} }{\cfrac{1}{cos(\theta )}-\cfrac{sin(\theta )}{cos(\theta )}\cdot sin(\theta )}\implies \cfrac{1}{cos(\theta )}-\cfrac{sin^2(\theta )}{cos(\theta )}\implies \cfrac{1-sin^2(\theta )}{cos(\theta )}\implies \cfrac{cos^2(\theta )}{cos(\theta )} \\\\\\ cos(\theta )\implies \cfrac{1}{sec(\theta )}`