Question

4sin30+tan48.tan42-3tan45​

Answer 1

$4 \sin30+ \tan48 \times \tan42 + 3 \tan45$

$4 (\frac{1}{ 2 }) + \tan(48) \times \tan(90 - 42) - 3(1)$

$2 + \tan(48) \times \ \cot(48) - 3$

$2 + \tan(48) \times \frac{1}{ \tan(48) } - 3$

$2+ 1 \times 1 - 3$

$3 \times (- 2)$

$- 6$

Answer 2

Given,

A trigonometric expression 4sin30+tan48.tan42-3tan45​

To Find,

The value of this expression.

Solution,

The given expression is

4sin30+tan48.tan42-3tan45​

4sin30+tan(90-42).tan42-3tan45

Now, using the fomula tan(90-x) = cot x

So,

4sin30+cot42.tan42-3tan45​​

4(1/2)+tan42/tan42-3(1)

2+1-3 = 0

Hence, the value 4sin30+tan48.tan42-3tan45​ is 0.