Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Students can Download Chapter 2 Inverse Trigonometric Functions Questions and Answers, Plus Two Maths Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Plus Two Maths Inverse Trigonometric Functions Three Mark Questions and Answers

Question 1.
Prove the following
Plus Two Maths Inverse Trigonometric Functions 3 Mark Questions and Answers 1
Answer:
Plus Two Maths Inverse Trigonometric Functions 3 Mark Questions and Answers 2

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions
Plus Two Maths Inverse Trigonometric Functions 3 Mark Questions and Answers 3
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Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Question 2.
Find the value of
Plus Two Maths Inverse Trigonometric Functions 3 Mark Questions and Answers 5
Answer:
Plus Two Maths Inverse Trigonometric Functions 3 Mark Questions and Answers 6

Question 3.
If tan-1x + tan-1y + tan-1z = π, show that x + y + z = xyz
Answer:
Given;
tan-1x + tan-1y + tan-1z = π
⇒ tan-1x + tan-1y = π – tan-1z
Plus Two Maths Inverse Trigonometric Functions 3 Mark Questions and Answers 7
⇒ x + y + z = xyz.

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Question 4.
Match the following
Plus Two Maths Inverse Trigonometric Functions 3 Mark Questions and Answers 8
Answer:
Plus Two Maths Inverse Trigonometric Functions 3 Mark Questions and Answers 9

Question 5.
Solve 2 tan-1(cos x) = tan-1(2 cos x)
Answer:
2 tan-1(cosx) = tan-1(2cosx)
⇒ \(\frac{2 \cos x}{1-\cos ^{2} x}\) = 2cosx
⇒ 1 = 1 – cos2 x ⇒ 1 = sin2x
⇒ x = ±\(\frac{\pi}{2}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Question 6.
Solve the following

  1. 2tan-1(cosx) = tan-1(2cosecx)
  2. tan-12x + tan-13x = \(\frac{\pi}{4}\)

Answer:
1. 2tan-1(cosx) = tan-1(2cosecx)
Plus Two Maths Inverse Trigonometric Functions 3 Mark Questions and Answers 10

2. tan-12x + tan-13x = \(\frac{\pi}{4}\)
Plus Two Maths Inverse Trigonometric Functions 3 Mark Questions and Answers 11
⇒ (6x – 1)(x + 1) = 0
⇒ x = \(\frac{1}{6}\), x = – 1
Since x = – 1 does not satisfy the equation, as the LHS becomes negative. So x = \(\frac{1}{6}\).

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Question 7.
Solve 2 tan-1(cos x) = tan-1(2 cos x)
Answer:
2 tan-1(cos x) = tan-1(2 cos x)
⇒ \(\frac{2 \cos x}{1-\cos ^{2} x}\) = 2cosx
⇒ 1 = 1 – cos2 x
⇒ 1 = sin2 x ⇒ x = ±\(\frac{\pi}{2}\)

Plus Two Maths Inverse Trigonometric Functions Four Mark Questions and Answers

Question 1.
Prove that \(\sin ^{-1} \frac{12}{13}+\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{63}{16}=\pi\)
Answer:
Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 12

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions
Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 13

Question 2.

  1. Find the principal value of sec-1\(\left(-\frac{2}{\sqrt{3}}\right)\) (1)
  2. if sin\(\left(\sin ^{-1}\left(\frac{1}{5}\right)+\cos ^{-1}(x)\right)=1\), then find the value of x. (3)

Answer:
1. principal value of:
Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 14

2. find the value of x:
Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 15

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Question 3.
Solve the following
Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 16
Answer:
Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 17

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions
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The value x = –\(\frac{\sqrt{3}}{\sqrt{28}}\) makes the LHS negative, so rejected.

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Question 4.
(i) Choose the correct answer from the bracket. cos(tan-1 x), |x| < 1 is equal to (1)
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Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 22
Answer:
Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 23
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(draw a right triangle to convert ‘tan’ to ‘sin’).

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Question 5.
(i) In which quadrants are the graph of cos-1 (x) lies, x ∈ [-1,1 ] (1)
(ii) If cos-1x + cos-1y = \(\frac{\pi}{3}\), then
sin-1x + sin-1y = ……… (3)
(a) \(\frac{2 \pi}{3}\)
(b) \(\frac{\pi}{3}\)
(c) \(\frac{\pi}{6}\)
(d) \(\frac{\pi}\)
(iii) If tan-1x + tan-1y = \(\frac{\pi}{4}\) then prove that x + y + xy = 1 (2)
Answer:
(i) First and Second quadrant
Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 27
Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 28
⇒ x + y = 1 – xy ⇒ x + y + xy = 1.

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Question 6.
(i) sin(tan-1(1)) is equal to
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Answer:
Plus Two Maths Inverse Trigonometric Functions 4 Mark Questions and Answers 31
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Plus Two Maths Inverse Trigonometric Functions Six Mark Questions and Answers

Question 1.
Show that sin-1\(\frac{3}{5}\) – sin-1\(\frac{8}{17}\) = cos-1\(\frac{84}{85}\).
Answer:
Plus Two Maths Inverse Trigonometric Functions 6 Mark Questions and Answers 34
Plus Two Maths Inverse Trigonometric Functions 6 Mark Questions and Answers 35
(draw a right triangle to convert ‘tan’ to ‘cos’).

Plus Two Maths Chapter Wise Questions and Answers Chapter 2 Inverse Trigonometric Functions

Question 2.
(i) Choose the correct answer from the Bracket.
If cos-1x = y, then y is equal to (1)
(a) π ≤ y ≤ π
(b) 0 ≤ y ≤ π
(c) \(-\frac{\pi}{2}\) ≤ y ≤ \(\frac{\pi}{2}\)
(d) 0 ≤ y ≤ π
(ii) Find the value of cos-1 cos\(\left(\frac{7 \pi}{3}\right)\) (3)
(iii) Solve for x if, tan-1\(\left(\frac{1+x}{1-x}\right)\) = 2 tan-1x (2)
Answer:
(i) Range of cos-1x is [0, π] ⇒ 0 ≤ y ≤ π

(ii) Here \(\left(\frac{7 \pi}{3}\right)\) lie outside the interval [0, π]. TO make it in the interval proceed as follows.
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Plus Two Maths Inverse Trigonometric Functions 6 Mark Questions and Answers 37

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