The value of $\frac{\sec ^2 60^{\circ} \cos ^2 45^{\circ}+{cosec}^2 30^{\circ}}{\cot 30^{\circ} \sec ^2 45^{\circ}-{cosec}^2 30^{\circ} \tan 45^{\circ}}$ is:
Answer & explanation
Correct answer: option 1
\(\frac{sec²60º cos²45º + cosec²30º}{cot30º.sec²45º - cosec²30º.tan45º}\)
= \(\frac{4 × 1/2 + 4 }{√3 × 2 - 4 × 1}\)
= \(\frac{6 }{2√3 - 4}\)
= \(\frac{3 }{√3 - 2}\)
Divide and multiply by ( √3 + 2 ).
= \(\frac{3 }{√3 - 2}\) × \(\frac{√3+ 2 }{√3 + 2}\)
= \(\frac{3 ( √3+ 2 ) }{3 - 4}\)
= - 3 ( √3+ 2 )