Question

Simplify this expression: cos theta/ tan theta cot theta

Answer 1

Q: $\frac{cos\theta}{tan\theta.cot\theta}=?$

A:

$\frac{cos\theta}{tan\theta.cot\theta}=cos\theta$

because... $tan\theta.cot\theta=1$
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Q: $\frac{cos\theta}{tan\theta}.cot\theta=?$

A:

$\frac{cos\theta}{tan\theta}.cot\theta&= \\ \\ \frac{cos\theta}{\frac{sin\theta}{cos\theta}}.\frac{cos\theta}{sin\theta}&= \\ \\ \frac{cos^2\theta}{sin\theta}}.\frac{cos\theta}{sin\theta}&= \\ \\ \frac{cos^3\theta}{sin^2\theta}}&= cos^3\theta.cosec^2\theta$