1.

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

Answer» Correct Answer - b
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`


Discussion

No Comment Found

Related InterviewSolutions