Find the value of x if 2 cosec2 30 + x sin2 60

Q) Find the value of X if 2 cosec²30⁰ + X sin² 60⁰ – (3\4) tan² 30⁰ = 10

Ans:

Given that, $2 \csc^2 30 + X \sin^260 - \frac{3}{4} \tan^230 = 10$

$2 (2)^2 + X (\frac{\sqrt3}{2})^2 - (\frac{3}{4}) (\frac{1}{\sqrt3})^2 = 10$

$X (\frac{3}{4}) - (\frac{3}{4}) (\frac{1}{3}) = 2$

$X (\frac{3}{4}) - \frac{1}{4} = 2$

$X (\frac{3}{4}) = 2 + \frac{1}{4} = \frac{9}{4}$

$X = 3$

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