simplify the following sin¯¹ (5/13 cosx …
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Posted by Yatin Jindal 8 years, 6 months ago
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Naveen Sharma 8 years, 6 months ago
Ans. Let {tex}y = sin^{-1} \left ( {5\over 13} cos x + {12\over 13} sinx \right ){/tex}
Put {tex}{5\over 13} = sin \ \alpha {/tex} = {tex}\alpha = sin^{-1} ({5\over 13}){/tex}
Then {tex}cos \ \alpha = \sqrt {1-sin^2 \ \alpha } = \sqrt {1-({5\over 13})^2}{/tex}
= {tex}\sqrt {1 - {25\over 169}} = \sqrt {144\over 125} = {12\over 13}{/tex}
Now,
=> {tex}y = sin^{-1} \left ( sin \ \alpha \ cos \ x + cos \ \alpha \ sin \ x \right ){/tex}
=> {tex}y = sin^{-1} \left ( sin(\alpha + x) \right ){/tex}
=> {tex}y = \alpha + x {/tex}
=> {tex}y = sin^{-1} ({5\over 13}) + x {/tex}
1Thank You