Question

8 2. PROVE: tane+cotes: sececsc? (Hint: Convert to sin's and cos's.

Answer 1

$\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1 \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf tan(\theta )+cot(\theta )=sec(\theta )csc(\theta ) \\\\[-0.35em] ~\dotfill\\\\ tan(\theta )+cot(\theta )\implies \cfrac{sin(\theta )}{cos(\theta )}+\cfrac{cos(\theta )}{sin(\theta )}\implies \cfrac{sin(\theta ) sin(\theta )+cos(\theta )cos(\theta )}{cos(\theta )sin(\theta )} \\\\\\ \cfrac{sin^2(\theta )+cos^2(\theta )}{cos(\theta )sin(\theta )}\implies \cfrac{1}{cos(\theta )sin(\theta )}\implies \cfrac{1}{cos(\theta )}\cdot \cfrac{1}{sin(\theta )}\implies sec(\theta )csc(\theta )$