Question

Find the principal value of cot inverse ✓3 - sec inverse (-2)

Answer 1

Answer:

Let tan

−1

3

=x that is

tanx=

3

=tan

3

π

Therefore, x=

3

π

∈[−

2

π

,

2

π

]

Now let sec

−1

(−2)=y that is secy=−2.

Therefore, y=−sec

3

π

that is

secy=sec(π−

3

π

)=sec

3

2π

Thus, y=

3

2π

∈[0,π]−(

2

π

)

Now consider tan

−1

3

−sec

−1

(−2) as shown below:

tan

−1

3

−sec

−1

(−2)=x−y=

3

π

−

3

2π

=−

3

π

Hence, tan

−1

3

−sec

−1

(−2)=−

3

π

.