Question

2 tan 30° / (1 − tan² 30°)
(a) cos 60° (b) sin 60° (c) tan 60° (d) sin30°

Answer 1

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Answer 2

Answer:

tan 60°

Step-by-step explanation:

We have to find the value of the following:

2 tan 30°/(1-tan² 30°)

Now, we have, 2 tan 30°/(1-tan² 30°)

=2(Sin 30°/Cos 30°)/{1-(Sin 30°/ Cos 30°)²}

=2 Sin 30° Cos 30°/ (Cos² 30°- Sin² 30°)

=Sin (2×30°)/ Cos (2×30°)

{We have used two formulas here. One is Sin 2α =2 Sin α Cos α and the other one is Cos 2α =Cos² α -Sin² α}

= Tan 60°.

So, option (c) is correct.