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Question
The value of cos248° – sin212° is ______.
[Hint: Use cos2A – sin2 B = cos(A + B) cos(A – B)]
Options
`(sqrt(5) + 1)/8`
`(sqrt(5) - 1)/8`
`(sqrt(5) + 1)/5`
`(sqrt(5) + 1)/(2sqrt(2)`
Solution
The value of cos248° – sin212° is `bbunderline((sqrt(5) + 1)/8)`.
Explanation:
The given expression is cos248° – sin212°.
cos248° – sin212° = cos(48° + 12°).cos(48° – 12°) ......[∵ cos2A – sin2B = cos(A + B).cos(A – B)]
= cos 60°.cos 36°
= `1/2 xx (sqrt(5) + 1)/4`
= `(sqrt(5) + 1)/8`
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