Question

evaluate tan−13​−sec−1(−2).​

Answer 1

Answer:

12th

Maths

Inverse Trigonometric Functions

Inverse Trigonometric Functions

Find the principal value of...

MATHS

Find the principal value of tan−13−sec−1(−2).

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ANSWER

Let tan−13=x that is 

tanx=3=tan3π

Therefore, x=3π∈[−2π,2π]

Now let sec−1(−2)=y that is secy=−2.

Therefore, y=−sec3π  that is 

secy=sec(π−3π)=sec32π 

Thus,  y=32π∈[0,π]−(2π