cos ( cot -1( textcosec( cos -1 a)))= (where 0

Question

cos ( cot -1( textcosec( cos -1 a)))= (where 0 < a < 1 ) (A) (1/√2-a2) (B) √3-a2 (C) √2-a2 (D) (1/√2+a2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/45388d617965903b40ef3aafd8b57c28-.png" /> Let cos -1 a=θ ⇒ cos θ=a ⇒ textcosec θ=(1/√1-a2) cos ( cot -1((1/√1-a2))) Let cot -1 (1/√1-a2)=φ ⇒ cot φ=(1/√1-a2) ⇒ cos φ=(1/√2-a2)

Q. $cos (cot^{- 1} (cosec (cos^{- 1} a))) =$ ______(where $0 < a < 1)$

$\frac{1}{2 - a ^{2}}$

$3 - a^{2}$

$2 - a^{2}$

$\frac{1}{2 + a ^{2}}$

Let $cos^{- 1} a = θ \Rightarrow cos θ = a$
$\Rightarrow cosec θ = \frac{1}{1 - a ^{2}}$
$cos (cot^{- 1} (\frac{1}{1 - a ^{2}}))$
Let $cot^{- 1} \frac{1}{1 - a ^{2}} = ϕ$
$\Rightarrow cot ϕ = \frac{1}{1 - a ^{2}}$
$\Rightarrow cos ϕ = \frac{1}{2 - a ^{2}}$

Q. cos(cot−1(cosec(cos−1a)))= ______(where 0<a<1)

2−a2​1​

3−a2​

2−a2​

2+a2​1​