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Question
If x tan 60° cos 60°= sin 60° cot 60°, then x = ______.
Options
cos 30°
tan 30°
sin 30°
cot 30°
Solution
If x tan 60° cos 60°= sin 60° cot 60°, then x = tan 30°.
Explanation:
Given, x tan 60° cos 60°= sin 60° cot 60°
x tan 60° cos 60°= sin 60° × `1/tan 60^circ`
Putting values
`x xx sqrt(3) xx 1/2 = sqrt(3)/2 xx 1/sqrt(3)`
`x xx sqrt(3)/2 = 1/2`
x = `1/2 xx 2/sqrt(3)`
x = `1/sqrt(3)`
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