If `3 sin_(theta)+5cos_(theta)=5` then the value of `5sin_(theta)-3cos_(theta) cos_(theta)` will be (यदि`3 sin_(theta)+5cos_(theta)=5` है तो `5sin_(theta)-3cos_(theta) cos_(theta)`का मान ज्ञात करे)

Options

A. `pm31`
B. `pm5`
C. `pm2`
D. `pm1`

Answer

a

Explanation

`sin theta+cos theta=sqrt(2)sin(90-theta)`
`sin theta+cos theta= sqrt(2)cos theta`
Divide both sides by `cos theta`
`tan theta+1=sqrt(2)`
`cot theta=(1)/(sqrt(2)-1)`
`=sqrt(2)+1`
`=sqrt(2)+1`