Question

Find the value of x for which x tan 45° cot 60° = sin 30° cosec 60°.

Answer 1

Given: x tan 45° cot 60° = sin 30° cosec 60°

tan 45° = 1, `cot 60^circ = 1/(tan 60^circ) = 1/sqrt(3)`.

Left side = `x xx 1 xx (1/sqrt(3)) = x/sqrt(3)`.

`sin 30^circ = 1/2, "cosec"  60^circ = 1/(sin 60^circ) = 2/sqrt(3)`.

Right side = `(1/2) xx (2/sqrt(3)) = 1/sqrt(3)`.

So `x/sqrt(3) = 1/sqrt(3) ⇒ x = 1`.