Question

Rewrite csc(theta) / sec(theta) as a single trig function with no fractions

Answer 1

The given expression is

`(\csc \theta)/(\sec \theta)`
`\text{ We know that }csc\theta=(1)/(\sin x)\text{ and }\sec \theta=(1)/(cos\theta)\text{.}`

Using the reciprocal, we get

`(\csc\theta)/(\sec\theta)=((1)/(\sin\theta))/((1)/(\cos \theta))`

`\text{ Use }((a)/(b))/((c)/(d))=(a)/(b)*(d)/(c)`

`(\csc\theta)/(\sec\theta)=(1)/(\sin\theta)*(\cos \theta)/(1)`
`\text{ Use }(\cos\theta)/(\sin\theta)=\cot \theta.`

`(\csc\theta)/(\sec\theta)=\cot \theta`

Hence the answer is

`\cot \theta`