Question

The value of `(3 tan 42^circ)/(cot 48^circ tan 60^circ)` is ______.

Options

• 9

• 1

• 3

• `sqrt(3)`

Answer 1

The value of `(3 tan 42^circ)/(cot 48^circ tan 60^circ)` is `underlinebb(sqrt(3))`.

Explanation:

Rewrite cot 48° as `1/(tan 48^circ)`.

So, the expression becomes `3 · tan 42° · (tan 48^circ)/(tan 60^circ)`.

Note tan 42° = tan (45° – 3°) and tan 48° = tan (45° + 3°).

The product tan (45° – x) · tan (45° + x) = 1. 

So, tan 42° · tan 48° = 1.

Therefore, the value = `3/(tan 60^circ)`

= `3/sqrt(3)`

= `sqrt(3)`