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INVERSE TRIGNOMETRIC FUNCTIONS Maths - INVERSE TRIGNOMETRIC FUNCTIONS

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 538 questions in this chapter.

Question types

INVERSE TRIGNOMETRIC FUNCTIONS question types

538 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

538
Questions
6
Question groups
5
Question types
Sample Questions

INVERSE TRIGNOMETRIC FUNCTIONS questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The principal value of $\tan^{-1}\Big(\tan\frac{3\pi}{5}\Big)$ is:
  1. $\frac{2\pi}{5}$
  2. $\frac{-2\pi}{5}$
  3. $\frac{3\pi}{5}$
  4. $\frac{-3\pi}{5}$
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Q 3M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options.

Which of the following is the principal value branch of cosec-1x?

  1. $\Big(\frac{-\pi}{2},\frac{\pi}{2}\Big)$

  2. $[0,\pi]-\Big\{\frac{\pi}{2}\Big\}$

  3. $\Big[\frac{-\pi}{2},\frac{\pi}{2}\Big]$

  4. $\Big[\frac{-\pi}{2},\frac{\pi}{2}\Big]-\{0\}$

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Q 4M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options.

The value of $\sin^{-1}\bigg[\cos\Big(\frac{33\pi}{5}\Big)\bigg]$ is:

  1. $\frac{3\pi}{5}$

  2. $\frac{-7\pi}{5}$

  3. $\frac{\pi}{10}$

  4. $\frac{-\pi}{10}$

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The solution of $\sin^{-1}(6\text{x})+\sin^{-1}(6\sqrt{3}\text{x})=\frac{-\pi}{2}$ is $\text{x}=\frac{1}{12}.$
Reason: $\cot^{-1}\text{x}$ is increasing function for $0\leq\text{x}\leq1.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false. 
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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If $0<\text{x}\leq\frac{\pi}{2},$ then $\sin^{-1}(\cos\text{x})+\cos^{-1}(\sin\text{x})=\pi-2\text{x}.$
Reason: $\cos^{-1}\text{x}=\frac{\pi}{2}-\sin^{-1}\text{x} $ for all $\text{x}\in[-1,1].$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
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Q 8Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\tan^{-1}\big[\text{x}+\sqrt{1+\text{x}^{2}}\big]=\frac{\pi}{2}-\frac{1}{2}\cot^{-1}.$
Reason: $\sin^{2}\Big[2\tan^{-1}\sqrt{\frac{1+\text{x}}{1-\text{x}}}\Big]=1-\text{x}^{2}.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
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Q 9Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\cos^{-1}\text{x}=2\sin^{-1}\sqrt{\frac{1-\text{x}}{2}}=2\cos^{-1}\sqrt{\frac{1+\text{x}}{2}}.$
Reason: $1+\cos\text{A}=2\cos^{2}\big(\frac{\text{A}}{2}\big)$ and $1-\cos\text{A}=2\sin^{2}\big(\frac{\text{A}}{2}\big).$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
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Q 10Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\cot\big[\frac{\pi}{2}-2\cot^{-1}3\big]=7.$
Reason: $\sin^{-1}\big(\frac{4}{5}\big)+2\tan^{-1}\big(\frac{1}{3}\big)=\frac{\pi}{2}.$ 
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false. 
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Q 111 Marks1 Mark
If $\tan^{-1}\text{x} +\tan^{-1}\text{y} = \frac{\pi}{4},\text{xy} < 1,$then write the value of x + y + xy.
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Q 151 Marks1 Mark
What is the principal value of cot-1 $\Bigg(\cos\frac{2\pi}{3}\Bigg)+\sin^{-1}\Bigg(\sin\frac{2\pi}{3}\Bigg)?$
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Q 162 Marks2 Marks
Prove that:
$3\sin^{-1}\text{x}=\sin^{-1}(3\text{x}-4\text{x}^3),\text{x}\in\Big[-\frac{1}{2},\frac{1}{2}\Big]$
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Q 182 Marks2 Marks
Evaluate the following:
$\cot^{-1}\frac{1}{\sqrt3}-\text{cosec}^{-1}(-2)+\sec^{-1}\Big(\frac{2}{\sqrt3}\Big)$
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Q 223 Marks3 Marks
If  $\tan^{-1} \frac{\text{x - 3}}{\text{x - 4}} + \tan^{-1} \frac{\text{x + 3}}{\text{x + 4}} = \frac{\pi}{4},$ then find the value of x.
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Q 274 Marks4 Marks
Show that $2\tan^{-1}\text{x}+\sin^{-1}\frac{2\text{x}}{1+\text{x}^2}$ is constant for $\text{x}\geq1,$ find that constant.
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