Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 4 Inverse Trigonometric Functions Ex 4.4 Textbook Questions and Answers, Notes.

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

Question 1.
Find the principle value of
(i) sec-1 (\(\frac {2}{√3}\))
(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 = \(\frac{\pi}{6}\)

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

(ii) cot-1 (√3)
cot-1 (√3) = θ
√3 = cot θ
cot \(\frac {π}{6}\) = cot θ
θ = \(\frac {π}{6}\)

(iii) cosec-1 (-√2)
cosec-1 (-√2) = θ
cosec θ = -√2 = -cosec(\(\frac {π}{4}\))
= cosec (-\(\frac {π}{4}\))
θ = –\(\frac {π}{4}\)

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

Question 2.
Find the value
(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(-\(\frac {√3}{2}\)) – sec-1(-√2)
Solution:
x = tan-1(√3)
tan x = √3 = tan \(\frac {π}{3}\)
x = \(\frac {π}{3}\)
y = sec-1(-2)
sec y = -2 = -sec \(\frac {π}{3}\)
sec y = sec(π – \(\frac {π}{3}\))
sec y = sec(2\(\frac {π}{3}\))
y = (2\(\frac {π}{3}\))
tan-1(√3) – sec-1(-2) = \(\frac {π}{3}\) – \(\frac {2π}{3}\)
= \(\frac {π – 2π}{3}\) = –\(\frac {π}{3}\)

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

(ii) sin-1(-1) + cos-1(\(\frac {1}{2}\)) + cot-1(2)
x = sin-1(1)
sin x = -1 = sin(-\(\frac {π}{2}\))
x = –\(\frac {π}{2}\)
y = cos-1(\(\frac {1}{2}\))
cos y = \(\frac {1}{2}\) = cos \(\frac {π}{3}\)
y = \(\frac {π}{3}\)
z = cot-1(2)
cot z = 2
z = cot-1(2) is constant.
sin-1(-1) + cos-1(\(\frac {1}{3}\)) + cot-1(2)
= –\(\frac {π}{2}\) + \(\frac {π}{3}\) + cot-1(2)
= –\(\frac {3π+2π}{6}\) + cot-1(2)
= cot-1(2) – \(\frac {π}{6}\)

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

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.4 1

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