NCERT Class 12-Mathematics: Chapter –2 Inverse Trigonometric Function Part 3

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Long Answer (L.A.)

Question 13:

Prove that

Answer:

Let then

Thus

Therefore,

Question 14:

Prove that

Answer:

We have

Question 15:

Which is greater,

Answer:

From Fig. 2.1, we note that tan is an increasing function in the interval This gives

Fig.2.1 - Increasing Function in the Interval

Fig.2.1 - Increasing Function in the Interval

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Question 16:

Find the value of

Answer:

Let and so that and .

Therefore,

Question 17:

Solve for

Answer:

From given equation, we have