Question

Sin square 30+cos square 45+sin square 60=3/2

Answer 1

${ \sin }^{2} 30 = { \frac{1}{2} }^{2} = \frac{1}{4} \\ \\ {cos}^{2} 45 = { \frac{1}{ \sqrt{2} } }^{2} = \frac{1}{2} \\ \\ \\ {sin}^{2}60 = { \frac{ \sqrt{3} }{2} }^{2} = \frac{3}{2} \\ \\ \\ \frac{1}{4} + \frac{1}{2} + \frac{3}{2} \\ \\ = \frac{1 + 2 + 6}{4} = \frac{9}{4}$

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Answer 2

$lhs \\ { \sin}^{2} (30) + { \cos }^{2} (45) + { \sin }^{2} (60) \\ = { (\frac{1}{2} )}^{2} + {( \frac{1}{ \sqrt{2} }) }^{2} + { (\frac{ \sqrt{3} }{2} )}^{2} \\ = \frac{1}{4} + \frac{1}{2} + \frac{3}{4} \\ = \frac{1 + 2 + 3}{4} \\ = \frac{6}{4 } \\ = \frac{3}{2}$
RHS
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