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

You can Download Samacheer Kalvi 12th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

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 sec²(cot^-1 3) + cosec² (tan^-1 2)
Solution:

Question 3.
Find the value of
Solution: