Question

If \[\frac{x {cosec}^2 30°\sec^2 45°}{8 \cos^2 45° \sin^2 60°} = \tan^2 60° - \tan^2 30°\] 

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Answer 1

We have: ` (xcosec^2 30° sec^2 45°)/ (8 cos^2 45° sin^2 60°)= tan ^2 60°-tan ^2 30°`

Here we have to find the value of x 

As we know that  `cos 45°=1/sqrt2 , sec 45°=sqrt2 , tan 30°=1sqrt3, tan 60°=sqrt3 , cos 30°=sqrt3/2, cose c 30°=2` 

So 

⇒`( x cosec^2 30° sec ^2 45°)/(8 cos^2 45° sin ^2 60)` 

⇒`( x xx4xx2)/(8xx1/2xx3/4)=3-1/3`

⇒ `(8x)/3=8/3`  

⇒ `x=1`