Question

If cos A=1/2
then evaluate sins quare A​

Answer 1

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Answer 2

$\color{red}\huge{\underline{\underline{\bf GIVEN\dag}}}$

$\cos(A)= \frac{1}{2}$

$\color{red}\huge{\underline{\underline{\bf SOLUTION\dag}}}$

$\sf \purple{we \: know \: that : }$

$\red{ \boxed{\sin ^{2} ( \theta) + \cos^{2} ( \theta) = 1}}$

$\implies \sin ^{2} (A ) + \cos^{2} (A)= 1$

$\implies\sin ^{2} (A ) + ( \cos A ) ^{2} = 1$

$\sf \purple{but : }$

$∵\cos A= \frac{1}{2}$

$\implies\sin ^{2} (A ) + ( \frac{1}{2} ) ^{2} = 1$

$\implies\sin ^{2} (A ) + \frac{1}{4} = 1$

$\implies\sin ^{2} (A ) = 1 - \frac{1}{4}$

$\orange{ \boxed{\therefore\sin ^{2} (A ) = \frac{3}{2} } }$

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