Evaluate: ^ -1 (-7 25 ) - Vidyadip

Question

Evaluate:
$\cos\Big\{\sin^{-1}\Big(-\frac{7}{25}\Big)\Big\}$

✓

Answer

$\cos\Big\{\sin^{-1}\Big(-\frac{7}{25}\Big)\Big\}$
$=\cos\Big\{-\sin^{-1}\Big(\frac{7}{25}\Big)\Big\}$
$=\cos\Big\{\sin^{-1}\Big(\frac{7}{25}\Big)\Big\}$
$=\cos\Big\{\cos^{-1}\sqrt{1-\big(\frac{7}{25}\big)^2}\Big\}$
$=\cos\Big\{\cos^{-1}\frac{24}{25}\Big\}$
$=\frac{24}{25}$

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