NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 8: Introduction to Trignometry and Its Applications
Exercise 8.1

MCQs on basic trigonometric ratios and identities, with brief justifications.

Question.  1

If \(\cos A = \dfrac{4}{5}\), then the value of \(\tan A\) is

(A)

\(\dfrac{3}{5}\)

(B)

\(\dfrac{3}{4}\)

(C)

\(\dfrac{4}{3}\)

(D)

\(\dfrac{5}{3}\)

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Question.  2

If \(\sin A=\dfrac{1}{2}\), then the value of \(\cot A\) is

(A)

\(\sqrt{3}\)

(B)

\(\dfrac{1}{\sqrt{3}}\)

(C)

\(\dfrac{\sqrt{3}}{2}\)

(D)

1

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Question.  3

The value of \([\csc(75^\circ+\theta)-\sec(15^\circ-\theta)-\tan(55^\circ+\theta)+\cot(35^\circ-\theta)]\) is

(A)

\(-1\)

(B)

0

(C)

1

(D)

\(\dfrac{3}{2}\)

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Question.  4

Given that \(\sin\theta=\dfrac{a}{b}\), then \(\cos\theta\) equals

(A)

\(\dfrac{b}{\sqrt{b^2-a^2}}\)

(B)

\(\dfrac{b}{a}\)

(C)

\(\dfrac{\sqrt{b^2-a^2}}{b}\)

(D)

\(\dfrac{a}{\sqrt{b^2-a^2}}\)

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Question.  5

If \(\cos(\alpha+\beta)=0\), then \(\sin(\alpha-\beta)\) can be reduced to

(A)

\(\cos\beta\)

(B)

\(\cos 2\beta\)

(C)

\(\sin\alpha\)

(D)

\(\sin 2\alpha\)

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Question.  6

The value of \(\tan1^\circ\tan2^\circ\tan3^\circ\,\cdots\,\tan89^\circ\) is

(A)

0

(B)

1

(C)

2

(D)

\(\dfrac{1}{2}\)

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Question.  7

If \(\cos9\alpha=\sin\alpha\) and \(9\alpha<90^\circ\), then the value of \(\tan5\alpha\) is

(A)

\(\dfrac{1}{\sqrt{3}}\)

(B)

\(\sqrt{3}\)

(C)

1

(D)

0

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Question.  8

If \(\triangle ABC\) is right angled at \(C\), then the value of \(\cos(A+B)\) is

(A)

0

(B)

1

(C)

\(\dfrac{1}{2}\)

(D)

\(\dfrac{\sqrt{3}}{2}\)

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Question.  9

If \(\sin A+\sin^2A=1\), then the value of \(\cos^2A+\cos^4A\) is

(A)

1

(B)

\(\dfrac{1}{2}\)

(C)

2

(D)

3

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Question.  10

Given \(\sin\alpha=\dfrac{1}{2}\) and \(\cos\beta=\dfrac{1}{2}\), the value of \(\alpha+\beta\) is

(A)

\(0^\circ\)

(B)

\(30^\circ\)

(C)

\(60^\circ\)

(D)

\(90^\circ\)

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Question.  11

The value of \(\left[\dfrac{\sin^2 22^\circ+\sin^2 68^\circ}{\cos^2 22^\circ+\cos^2 68^\circ}+\sin^2 63^\circ+\cos63^\circ\sin27^\circ\right]\) is

(A)

3

(B)

2

(C)

1

(D)

0

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Question.  12

If \(4\tan\theta=3\), then \(\dfrac{4\sin\theta-\cos\theta}{4\sin\theta+\cos\theta}\) equals

(A)

\(\dfrac{2}{3}\)

(B)

\(\dfrac{1}{3}\)

(C)

\(\dfrac{1}{2}\)

(D)

\(\dfrac{3}{4}\)

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Question.  13

If \(\sin\theta-\cos\theta=0\), then the value of \(\sin^4\theta+\cos^4\theta\) is

(A)

1

(B)

\(\dfrac{3}{4}\)

(C)

\(\dfrac{1}{2}\)

(D)

\(\dfrac{1}{4}\)

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Question.  14

\(\sin(45^\circ+\theta)-\cos(45^\circ-\theta)\) equals

(A)

\(2\cos\theta\)

(B)

0

(C)

\(2\sin\theta\)

(D)

1

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Question.  15

A pole 6 m high casts a shadow \(2\sqrt{3}\) m long on the ground. The Sun’s elevation is

(A)

\(60^\circ\)

(B)

\(45^\circ\)

(C)

\(30^\circ\)

(D)

\(90^\circ\)

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NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 8: Introduction to Trignometry and Its Applications – Exercise 8.1 | Detailed Answers