Exercise 4.4 - Chapter 4 - Trigonometry - 11th Business Maths Guide Samacheer Kalvi Solutions

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Exercise 4.4

 Text Book Back Questions and Answers

Question 1.
Find the principal value of the following:

Solution:

Question 2.
Prove that

Solution:
(i) Let tan^-1 x = θ
x = tan θ

Question 3.
Show that

Solution:
We know that tan^-1 x + tan^-1 y 

Question 4.

Solution:

⇒ 5x = 1(1 – 6x²)
⇒ 6x² + 5x – 1 = 0
⇒ (x + 1) (6x – 1) = 0
⇒ x + 1 = 0 (or) 6x – 1 = 0
⇒ x = -1 (or) x = 1/6
x = -1 is rejected. It doesn’t satisfies the question.
Note: Put x = -1 in the given question.

So the question changes.

Question 5.
Solve: tan^-1 (x + 1) + tan^-1 (x – 1)

Solution:

⇒ 7x = 2(2 – x²)
⇒ 7x = 4 – 2x²
⇒ 2x² + 7x – 4 = 0
⇒ (x + 4) (2x – 1) = 0
⇒ x + 4 = 0 (or) 2x – 1 = 0
⇒ x = -4 (or) x = 1/2
x = -4 is rejected, since does not satisfies the question.
∴ x = ½

Question 6.
Evaluate

Solution:

Question 7.
Evaluate: 

Solution:

Question 8.

Solution:

Question 9.
Show that

Solution:

Question 10.
Express 
 in the simplest form.
Solution: