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## Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.4

Question 1.

Find the principal value of

(i) sec^{-1 }(\(\frac{2}{\sqrt{3}}\))

(ii) cot^{-1}(√3)

(iii) cosec^{-1}(-√2)

Solution:

(i) Let sec^{-1} (\(\frac{2}{\sqrt{3}}\)) = θ

⇒ sec θ = \(\frac{2}{\sqrt{3}}\)

⇒ cos θ = \(\frac{\sqrt{3}}{2}\) = cos \(\frac{\pi}{6}\)

⇒ θ = \(\frac{\pi}{6}\)

(ii) Let cot^{-1}(√3) = θ

⇒ cot θ = √3

⇒ tan θ = \(\frac{1}{\sqrt{3}}\) = tan \(\frac{\pi}{6}\)

⇒ θ = \(\frac{\pi}{6}\)

(iii) Let cosec^{-1} (-√2) = θ

⇒ cosec θ = -√2

⇒ sin θ = \(-\frac{1}{\sqrt{2}}\)

⇒ θ = \(-\frac{\pi}{4}\)

Question 2.

Find the value of

(i) tan^{-1}(√3) – sec^{-1}(-2)

(ii) sin^{-1}(-1) + cos^{-1} (\(\frac{1}{2}\)) + cot^{-1}(2)

(iii) cot^{-1}(1) + sin^{-1}(\(-\frac{\sqrt{3}}{2}\)) – sec^{-1}(-√2)

Solution:

### Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.4 Additional Problems

Question 1.

Find the principal value of the following

Solution:

Question 2.

Find the value of sec^{2}(cot^{-1} 3) + cosec^{2} (tan^{-1} 2)

Solution:

Question 3.

Find the value of

Solution: