cosec[2cot⁻¹(5)+cos⁻¹(4/5)] value... | Trigonometry

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JEE MAIN 2021

25-02-2021 S2

Question

$\operatorname{cosec}\left[2 \cot ^{-1}(5)+\cos ^{-1}\left(\frac{4}{5}\right)\right]$ is equal to :

Select the correct option:

$\frac{56}{33}$

$\frac{65}{56}$

$\frac{65}{33}$

$\frac{75}{56}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & \operatorname{cosec}\left[2 \tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{3}{4}\right)\right] \\ & \operatorname{cosec}\left[\tan ^{-1}\left(\frac{5}{12}\right)+\tan ^{-1}\left(\frac{3}{4}\right)\right] \\ & =\operatorname{cosec}\left[\tan ^{-1}\left(\frac{56}{33}\right)\right]=\frac{65}{56}\end{aligned}$

Question Tags

JEE Main

Mathematics

Easy

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