QJEEM21Ma40b8: JEE Main 2021 Mathematics - Class 12 JEEM21Ma40b8 Solution: If ; , then the value of is :

Question

Verified Solution • 2025–26 Session moderate

If

{{{{\sin }^1}x} \over a} = {{{{\cos }^{ - 1}}x} \over b} = {{{{\tan }^{ - 1}}y} \over c}

;

0 &lt; x &lt; 1

,
then the value of

\cos \left( {{{\pi c} \over {a + b}}} \right)

is :

Accepted Answer

{{{{\sin }^{ - 1}}x} \over a} = {{{{\cos }^{ - 1}}x} \over b} = {{{{\tan }^{ - 1}}y} \over c}

{{{{\sin }^{ - 1}}x} \over a} = {{{{\cos }^{ - 1}}x} \over b} = {{{{\sin }^{ - 1}}x + {{\cos }^{ - 1}}x} \over {a + b}} = {\pi \over {2(a + b)}}

Now,

{{{{\tan }^{ - 1}}y} \over c} = {\pi \over {2(a + b)}}

2{\tan ^{ - 1}}y = {{\pi c} \over {a + b}}

\Rightarrow \cos \left( {{{\pi c} \over {a + b}}} \right) = \cos (2{\tan ^{ - 1}}y) = {{1 - {y^2}} \over {1 + {y^2}}}

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