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The value of f(alpha)=sqrt(cos e c^2alph...

The value of `f(alpha)=sqrt(cos e c^2alpha-2cotalpha)+sqrt(cos e c^2alpha+2cotalpha)` can be

A

`2cotalpha`

B

`-2cotalpha`

C

2

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`f(alph)=sqrt(cosec^2alpha-2cotalpha)+sqrt(cosec^2alpha+2cotalpha)`
`=sqrt(1+cot^2alpha-2cotalpha)+sqrt(cosec^2lpha+2cotalpha)`
`=abs(cotalpha-1)=abs(cotalpha+1)`
Case I : `cotalphale-1`
`:. f(alpha)=-cotalpha=1-cotalpha-1=-2cotalpha`
Case II : `-1lecotalphale1`
`:. f(alpha)=-cotalpha+1+cotalpha+1=2`
Case III : `cotalphage 1`
`:. f(alpha)=(cotalpha-1)+(cotalpha+1)=2cotalpha`
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