Evaluate : ( 30^ + 45^ ) ( 60^ - 459 ) - Vidyadip

MCQ

Evaluate : $\left(\sin 30^{\circ}+\sin 45^{\circ}\right)\left(\cos 60^{\circ}-\cos 459\right)$

A
$\frac{5}{8}$
B
$\frac{-5}{8}$
C
$\frac{1}{2}$
D
$\frac{-1}{2}$

✓

Answer

(d) : We have, $\left(\sin 30^{\circ}+\sin 45^{\circ}\right)\left(\cos 60^{\circ}-\cos 45^{\circ}\right)$
$=\left(\frac{1}{2}+\frac{1}{\sqrt{2}}\right)\left(\frac{1}{2}-\frac{1}{\sqrt{2}}\right)=\left(\frac{1}{2}\right)^2-\left(\frac{1}{\sqrt{2}}\right)^2=\left(\frac{1}{4}-\frac{1}{2}\right)=\frac{-1}{2}$

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