Question

Prove `cot theta+tan theta=(cosec theta)(sec theta)` by completing the following activity: LHS`=cot theta+tan theta` `=(cos theta)/(sin theta)+(square)/(cos theta)` `=(square +square)/(sin thetaxx co cos theta)` `=(square)/(sin thetaxx cos theta)` `=1/(square)xx1/(square)` `=cosec thetaxx sec theta` `=RHS` `:.cot theta+tan theta=cosec thetaxx sec theta`

Answer 1

Activity:
`LHS=cot theta+tan theta`
`=(cos theta)/(sin theta)+(sin theta)/(cos theta)`
`=(cos^(2) theta+sin^(2) theta)/(sin thetaxx cos theta)`
`=1/(sin thetaxx cos theta)`
`=1/(sin theta)xx1/(cos theta)`
`=cosec thetaxx sec theta`
`=RHS`
`:.cot theta+tan theta=cosec thetaxx sec theta`.