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

Question

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

The value of `f(alpha)=sqrt(cos e c^2alpha-2cotalpha)+sqrt(cos e c^2alpha+2cotalpha)` can be `2cotalpha` (b) `-2cotalpha` (c) 2 (d) `-2`
A. `2cotalpha`
B. `-2cotalpha`
C. 2
D. `-2`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - 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`