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Trigonometry — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsTrigonometry2 Marks
Question
Find the values of : $\cos ^2 45^{\circ}+\sin ^2 30^{\circ}$
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Answer

$\cos ^2 45^{\circ}+\sin ^2 30^{\circ}$
$\cos 45^{\circ}=\frac{1}{\sqrt{2}} \text { and } \sin 30^{\circ}=\frac{1}{2}$
$\cos ^2 45^{\circ}+\sin ^2 30^{\circ}=\left(\cos 45^{\circ}\right)^2+\left(\sin 30^{\circ}\right)^2$
$=\left(\frac{1}{\sqrt{2}}\right)^2+\left(\frac{1}{2}\right)^2$
$=\frac{1}{2}+\frac{1}{4}$
$=\frac{2+1}{4}$
$\therefore \quad \cos ^2 45^{\circ}+\sin ^2 30^{\circ}=\frac{3}{4}$

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