If (x-xcosec²30°)/(1+cosec²30°)=cos²60°+4cot²45°-sec²60° ,then the value of x is _.

If (x-xcosec²30°)/(1+cosec²30°)=cos²60°+4cot²45°-sec²60°…

If $\frac{x-xcosec^230°}{1+cosec^230°}=cos^260°+4cot^245°-sec^260°$ ,then the value of x is _____.

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. - $\frac{5}{12}$

We know, cosec(30)° = 2

cos(60)° = 1/2

cot(45)° = 1

sec(60)° = 2

Thus we can now solve this equation as,

{x - x(2)²}/{1 + 2²} = 1/4 + 4 - 4

⇒ -3x/5 = 1/4

⇒ x = -5/12