Question

Verify that each equation is an identity.

tan+1/sec = sin+ cos

Answer 1

`\cfrac{tan(\theta )+1}{sec(\theta )}~~ = ~~sin(\theta )+cos(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{tan(\theta )+1}{sec(\theta )}\implies \cfrac{~~ ( sin(\theta ))/(cos(\theta ) ) +1~~}{(1)/(cos(\theta ))}\implies \cfrac{~~ ( sin(\theta )+cos(\theta ))/(cos(\theta ) ) ~~}{(1)/(cos(\theta ))}`

`\cfrac{ sin(\theta )+cos(\theta )}{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ } \cdot \cfrac{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1}\implies sin(\theta )+cos(\theta )`