Question

sin theta = x , sec theta =y . find cot theta pls answer fast i need to verify my answer . you can directly write the answer no issues

Answer 1

`\huge\boxed{\cot\theta=(1)/(xy)}`

Explanation:

`\bold{METHOD\ 1}`

`\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=(1)/(\cos x);\ \cot x=(\cos x)/(\sin x)\\\\\sec\theta=y\to(1)/(\cos \theta)=y\to(\cos\theta)/(1)=(1)/(y)\to\cos\theta=(1)/(y)\\\\\cot \theta=((1)/(y))/(x)=(1)/(xy)`

`\bold{METHOD\ 2}`

`\text{We know}\\\\\tan x=(\sin x)/(\cos x)\\\\\cot x=(\cos x)/(\sin x)=(1)/(\tan x)\\\\\sec x=(1)/(\cos x)\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left((1)/(\cos x)\right)=(\sin x)/(\cos x)=\tan x\\\\(1)/((\sin x)(\sec x))=(1)/(\tan x)=\cot x`

`\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=(1)/(xy)`