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Question
Find the value of x, if cos (2x – 6) = cos2 30° – cos2 60°
Solution
cos (2x – 6) = cos2 30° – cos2 60°
cos (2x – 6) = cos2 (90° – 60°) – cos2 60°
cos (2x – 6) = sin2 60° – cos2 60°
cos (2x – 6) = 1 – 2 cos2 60°
= `1 - 2(1/2)^2`
= `1 - 1/2`
= `1/2`
cos (2x – 6) = `1/2`
cos (2x – 6) = cos 60°
(2x – 6) = 60°
2x = 66°
Hence, x = 33°
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