Inverse Trigonometric Functions Online Objective Test | Inverse Trigonometric Functions Online Objective Test

# Inverse Trigonometric Functions # CBSE 12th Mathematics Prepare / Learn

Q1. If

c o s^{(- 1)} x + c o s^{(- 1)} y = 2 π

, then the value of

s i n^{(- 1)} x + s i n^{(- 1)} y

A. −π

B. 0

C. None of these

D. π

Answer : Option A
Explaination / Solution:

# Inverse Trigonometric Functions # CBSE 12th Mathematics Prepare / Learn

Q2. if

θ = c o s^{(- 1)} (\frac{1}{x}),

then tan θ is equal to

A. none of these

B. √x² - 1

C. 1−x2√x

D. x1−x2√|x|

Answer : Option C
Explaination / Solution:

# Inverse Trigonometric Functions # CBSE 12th Mathematics Prepare / Learn

Q3. If

c o s (2 s i n^{- 1} x) = \frac{1}{9}

then x =

A. none of these

B. ±2/3

C. 2/3

D. -2/3

Answer : Option B
Explaination / Solution:

# Inverse Trigonometric Functions # CBSE 12th Mathematics Prepare / Learn

Q4.

2 \cos^{- 1} x = \cos^{- 1}

(2 x^{2} - 1)

holds true for all

A. |x|⩽12

B. |x|⩽1

C. none of these.

D. 0⩽x⩽1

Answer : Option D
Explaination / Solution:

This is true for all real values of x ∈[0,1].

# Inverse Trigonometric Functions # CBSE 12th Mathematics Prepare / Learn

Q5.

\cos^{- 1} (\cos x) = x

is satisfied by ,

A. x∈[−1,1],

B. x∈[0,1]

C. x∈[0,π]

D. none of these.

Answer : Option C
Explaination / Solution:

\cos^{- 1} (\cos x) = x

if ,

0 ⩽ x ⩽ π

i.e. if ,

x \in [0, π]

# Inverse Trigonometric Functions # CBSE 12th Mathematics Prepare / Learn

Q6.

\tan^{- 1} \frac{1}{7} + 2 \tan^{- 1} \frac{1}{3}

is equal to

A. none of these.

B. π/2

C. π/4

D. 3π/4

Answer : Option C
Explaination / Solution:

# Inverse Trigonometric Functions # CBSE 12th Mathematics Prepare / Learn

Q7. The value of

\tan^{- 1} (\frac{a}{b}) - \tan^{- 1} (\frac{a - b}{a + b})

(a, b > 0)

A. −π/2

B. π/2

C. −π/4

D. π/4

Answer : Option D
Explaination / Solution:

# Inverse Trigonometric Functions # CBSE 12th Mathematics Prepare / Learn

Q8. If

x > 0,

then

\tan^{- 1} x + \tan^{- 1} (\frac{1}{x})

is equal to

A. π/2

B. 1

C. None of these

D. tan 1

Answer : Option A
Explaination / Solution:

tan−1x+tan−1(1x)tan−1x+cot−1x=π2

# Inverse Trigonometric Functions # CBSE 12th Mathematics Prepare / Learn

Q9. Which of the following is different from

2 \tan^{- 1} x

A. sin−1(2x1−x2),|x|⩽1

B. None of these

C. cos−1(1−x21+x2),|x|⩾0

\tan^{- 1} (\frac{2 x}{1 - x^{2}}), | x | < 1

Answer : Option B
Explaination / Solution:

therefore , none of these is the right option.

# Inverse Trigonometric Functions # CBSE 12th Mathematics Prepare / Learn

Q10.

3 \sin^{- 1} x = \sin^{- 1}

(3 x - 4 x^{3})

holds good for all

A. none of these

B. |x|⩽1

C. 0⩽x⩽1

D. |x|⩽1/2

Answer : Option D
Explaination / Solution:

Total Question/Mark :
Scored Mark :
Mark for Correct Answer : 1
Mark for Wrong Answer : -0.5
Mark for Left Answer : 0

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