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Question
If tan2 45° − cos2 30° = x sin 45° cos 45°, then x =
Options
2
−2
\[- \frac{1}{2}\]
\[\frac{1}{2}\]
Solution
We are given:` tan^2 45°-cos^2 30°=x sin 45° cos 45°`
We have to find x
⇒` 1-(sqrt3/2)^2=x 1/sqrt2 xx1/sqrt2`
⇒ `1-3/4=x/2`
⇒ `1/4=x/2`
⇒`x=1/2`
We know that ` sin°45=1/sqrt2 , cos 45°=1/sqrt2, tan 45°=1, cos 30°=sqrt3/2`
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