Question

Simplify this expression: cos theta/ tan theta cot theta

Answer 1

Q:
`(cos\theta)/(tan\theta.cot\theta)=?`

A:


`(cos\theta)/(tan\theta.cot\theta)=cos\theta`

because...
`tan\theta.cot\theta=1`
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Q:
`(cos\theta)/(tan\theta).cot\theta=?`

A:


`(cos\theta)/(tan\theta).cot\theta&= \\ \\ (cos\theta)/((sin\theta)/(cos\theta)).(cos\theta)/(sin\theta)&= \\ \\ (cos^2\theta)/(sin\theta)}.(cos\theta)/(sin\theta)&= \\ \\ (cos^3\theta)/(sin^2\theta)}&= cos^3\theta.cosec^2\theta`