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Question
Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°
Solution
cos2x = cos60° cos30° + sin60° sin30°
⇒ cos2x = `(1)/(2) xx sqrt(3)/(2) + sqrt(3)/(2) xx (1)/(2)`
⇒ cos2x = `sqrt(3)/(4) + sqrt(3)/(4)`
⇒ cos2x = `(2sqrt(3))/(4)`
⇒ cos2x = `sqrt(3)/(2)`
⇒ cos2x = cos30°
⇒ 2x = 30°
⇒ x = 15°.
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