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3.Trigonometrical Ratios, Functions and Identities
hard
$ \cos ^{3}\left(\frac{\pi}{8}\right) \cdot \cos \left(\frac{3 \pi}{8}\right)+\sin ^{3}\left(\frac{\pi}{8}\right) \cdot \sin \left(\frac{3 \pi}{8}\right)$ ની કિમંત મેળવો.
A
$\frac{1}{4}$
B
$\frac{1}{\sqrt{2}}$
C
$\frac{1}{2\sqrt{2}}$
D
$\frac{1}{2}$
(JEE MAIN-2020)
Solution
$\cos ^{3} \frac{\pi}{8} \cdot \sin \frac{\pi}{8}+\sin ^{3} \frac{\pi}{8} \cdot \cos \frac{\pi}{8}$
$=\sin \frac{\pi}{8} \cdot \cos \frac{\pi}{8}=\frac{1}{2} \sin \frac{\pi}{4}=\frac{1}{2 \sqrt{2}}$
Standard 11
Mathematics
