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Find the principal value of sin-1(√3-1/2√2)

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Find the principal value of sin^-1(√3-1/2√2)

Posted by Kadam Cool 8 years, 1 month ago

CBSE > Class 12 > Mathematics

1 answers

Varun Arora 7 years, 11 months ago

$\begin{array}{l} {\sin ^{ - 1}}\left( {\frac{{\sqrt 3 }}{2}\frac{1}{{\sqrt 2 }} - \frac{1}{2}\frac{1}{{\sqrt 2 }}} \right)\\ = {\sin ^{ - 1}}\left[ {\sin \frac{\pi }{3}\cos \frac{\pi }{4} - \cos \frac{\pi }{3}\sin \frac{\pi }{4}} \right] \end{array}$

$\Rightarrow {\sin ^{ - 1}}\left[ {\sin \left( {\frac{\pi }{3} - \frac{\pi }{4}} \right)} \right] = \frac{\pi }{{12}}$ $As,\,{\sin ^{ - 1}}(\sin x) = x\,for\,all\,x\, \in \left[ {\frac{{ - \pi }}{2},\frac{\pi }{2}} \right]$

5Thank You

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