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Question

Mathematics Question on Trigonometric Functions

The value of cos 210∘−cos10∘cos50∘+cos250∘^2 10^{\circ} - cos10^{\circ} cos50^{\circ} + cos^2 50^{\circ}

A

32(1+cos20∘)\frac{3}{2}(1+cos 20^{\circ})

B

34\frac{3}{4}

C

34+cos20∘\frac{3}{4} + cos 20^{\circ}

D

32\frac{3}{2}

Answer

34\frac{3}{4}

Explanation

Solution

12(2cos210∘−2cos10∘cos50∘∣+2cos250∘)\frac{1}{2} (2 cos^2 10^{\circ} - 2 cos 10^{\circ} cos 50^{\circ} | + 2 cos^2 50^{\circ}) ⇒  12(1+cos20∘−(cos60∘+cos40∘)+1+cos100∘)\Rightarrow \, \, \frac{1}{2} (1 + cos 20^{\circ}- (cos60^{\circ} + cos40^{\circ}) + 1 + cos100^{\circ}) ⇒  12(32+cos20∘+2sin70∘sin(−30∘))\Rightarrow \, \, \frac{1}{2} \bigg(\frac{3}{2}+ cos 20^{\circ} + 2 sin 70^{\circ} sin (-30^{\circ})\bigg) ⇒  12(32+cos20∘−sin70∘)\Rightarrow \, \, \frac{1}{2} \bigg(\frac{3}{2} + cos 20^{\circ} - sin 70^{\circ}\bigg) ⇒ 34\Rightarrow \, \frac{3}{4}