simplify the following sin¯¹ (5/13 cosx …

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simplify the following

sin¯¹ (5/13 cosx + 12/13 sinx)

Posted by Yatin Jindal 8 years, 1 month ago

CBSE > Class 12 > Mathematics

1 answers

Naveen Sharma 8 years, 1 month ago

Ans. Let $y = sin^{-1} \left ( {5\over 13} cos x + {12\over 13} sinx \right )$

Put ${5\over 13} = sin \ \alpha$ = $\alpha = sin^{-1} ({5\over 13})$

Then $cos \ \alpha = \sqrt {1-sin^2 \ \alpha } = \sqrt {1-({5\over 13})^2}$

= $\sqrt {1 - {25\over 169}} = \sqrt {144\over 125} = {12\over 13}$

Now,

=> $y = sin^{-1} \left ( sin \ \alpha \ cos \ x + cos \ \alpha \ sin \ x \right )$

=> $y = sin^{-1} \left ( sin(\alpha + x) \right )$

=> $y = \alpha + x$

=> $y = sin^{-1} ({5\over 13}) + x$

1Thank You

ANSWER

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