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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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Solution
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`
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