if `1+cos^(2)theta=3sinthetacostheta` then the integral value of `cottheta` is `(0 lt theta lt (pi)/(2))`

Options

A. 2
B. 1
C. 3
D. 0

Answer

b

Explanation

Given, `1+cos^(2)theta=3sintheta.cos theta`
`[Oltthetaltpi//2]`
` 1+cos^(2)theta=3sin theta.cos theta`
Dividing by `sin^(2)theta.cos theta`
`rArrco s ec^(2)theta+cot^(2)theta=3cottheta`
`rArr1+cot^(2)theta+cot^(2)theta=3cottheta`
`because [1+cot^(2)theta=co s ec^(2)theta]`
`rArr1+2cot^(2)theta=3cottheta`
`rArr2cot^(2)theta=3cottheta-1`
Let `theta=45^(@)`
`because Cot 45^(@)=1`
`2cot^(2)45^(@)-3cot45^(@)+1=0`
2-3+1=0
0=0
Therefore `cot theta=cot45^(@)=1`