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3.Trigonometrical Ratios, Functions and Identities
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કિંમત શોધો : $\sin 75^{\circ}$
A
$\frac{\sqrt{3}+1}{2 \sqrt{2}}$
B
$\frac{\sqrt{3}+1}{2 \sqrt{2}}$
C
$\frac{\sqrt{3}+1}{2 \sqrt{2}}$
D
$\frac{\sqrt{3}+1}{2 \sqrt{2}}$
Solution
$\sin 75^{\circ}=\sin \left(45^{\circ}+30^{\circ}\right)$
$=\sin 45^{\circ} \cos 30^{\circ}+\cos 45^{\circ} \sin 30^{\circ}$
$[\sin (x+y)=\sin x \cos y+\cos x \sin y]$
$=\left(\frac{1}{\sqrt{2}}\right)\left(\frac{\sqrt{3}}{2}\right)+\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{2}\right)$
$=\frac{\sqrt{3}}{2 \sqrt{2}}+\frac{1}{2 \sqrt{2}}=\frac{\sqrt{3}+1}{2 \sqrt{2}}$
Standard 11
Mathematics
