cos(2 cos-1 (1/5)+ sin-1 (1/5)) is euqal to

Question

cos(2 cos-1 (1/5)+ sin-1 (1/5)) is euqal to (A)  (1/5) (B)  (-2√ 6/5) (C) - (1/5) (D)  (√ 6 /5)

Tardigrade Admin · Accepted Answer

cos 2 cos -1 (1/5)+ sin -1 (1/5) = cos cos -1 (1/5)+( cos -1 (1/5)+ sin -1 (1/5)) = cos cos -1 (1/5)+(π/2) (∵ sin -1 x+ cos -1 x=(π/2), ∀ x ∈ R) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/bc4139e37856f0c7b5d1cc61902f4244-.png" /> = cos ((π/2)+ cos -1 (1/5)) =- sin ( cos -1 (1/5)) =- sin ( sin -1 (√24/5)) =-(2 √6/5)

Q. $cos (2 cos^{- 1} \frac{1}{5} + sin^{- 1} \frac{1}{5})$ is euqal to

$\frac{1}{5}$

$\frac{- 2 6}{5}$

$- \frac{1}{5}$

$\frac{6}{5}$

Q. cos(2cos−151​+sin−151​) is euqal to

51​

5−26​​

−51​

56​​

cos{2cos−151​+sin−151​} =cos{cos−151​+(cos−151​+sin−151​)} =cos{cos−151​+2π​} (∵sin−1x+cos−1x=2π​,∀x∈R) =cos(2π​+cos−151​) =−sin(cos−151​) =−sin(sin−1524​​) =−526​​

Q. $cos (2 cos^{- 1} \frac{1}{5} + sin^{- 1} \frac{1}{5})$ is euqal to

$\frac{1}{5}$

$\frac{- 2 6}{5}$

$- \frac{1}{5}$

$\frac{6}{5}$