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

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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) sec-1 (\(\frac {2}{√3}\)) = θ
sec θ = \(\frac {2}{√3}\) = sec \(\frac {π}{6}\)
θ = \(\frac {π}{6}\)

(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 Q2
Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.4 Q2.1

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

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

Question 1.
Find the principal value of the following
Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.4 1
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.4 2
Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.4 3

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

Question 2.
Find the value of sec2(cot-1 3) + cosec2 (tan-1 2)
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.4 4

Question 3.
Find the value of Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.4 5
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.4 55

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