(A) Given expression: $\sin^{2} 30^{\circ} - \tan 45^{\circ} + \cos^{2} 60^{\circ} - \cot 90^{\circ}$Substitute the trigonometric values:$\sin 30^{\ci

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(A) Given expression: $\sin^{2} 30^{\circ} - \tan 45^{\circ} + \cos^{2} 60^{\circ} - \cot 90^{\circ}$Substitute the trigonometric values:$\sin 30^{\circ} = \frac{1}{2}$,$\tan 45^{\circ} = 1$,$\cos 60^{\circ} = \frac{1}{2}$,and $\cot 90^{\circ} = 0$Substituting these values into the expression:$= (\frac{1}{2})^{2} - 1 + (\frac{1}{2})^{2} - 0$$= \frac{1}{4} - 1 + \frac{1}{4}$$= \frac{2}{4} - 1$$= \frac{1}{2} - 1$$= -\frac{1}{2}$

Class 10 Mathematics Introduction to Trigonometry Mix Examples - Introduction to Trigonometry

Easy

The value of $\sin^{2} 30^{\circ} - \tan 45^{\circ} + \cos^{2} 60^{\circ} - \cot 90^{\circ}$ is ........

A
$-\frac{1}{2}$
B
$1$
C
$\frac{3}{2}$
D
$2$

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Class 10 Questions

Class 10

Mathematics Questions

Chapter

Introduction to Trigonometry

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Mix Examples - Introduction to Trigonometry

Which of the following pairs is correct for trigonometric inter-relationships?

$1. \cos \theta$ $a. \frac{\cos \theta}{\sin \theta}$

$2. \tan \theta$ $b. \frac{1}{\csc \theta}$

$3. \cot \theta$ $c. \frac{1}{\sec \theta}$

$4. \sin \theta$ $d. \frac{1}{\cot \theta}$

$e. \sin \theta \cdot \cos \theta$

Easy

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If $\sec 4A = \operatorname{cosec}(A - 20^\circ)$,where $4A$ is an acute angle,then the value of $A$ is $\ldots \ldots \ldots \ldots .$ (in $^\circ$)

Medium

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If $\sin ^{2}(3 x+30^{\circ})+\cos ^{2}(2 x+45^{\circ})=1$,then $x = \dots$ (in $^{\circ}$)

Easy

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If $\sin 5 \theta = \cos 5 \theta$,then the value of $\theta$ is ..........

Medium

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Which of the following groups truly matches the data of Part $I$ with the data of Part $II$?

Part $I$ Part $II$

$1.$ $\cos(90^\circ - \theta)$ $a.$ $\sec \theta$

$2.$ $\cot(90^\circ - \theta)$ $b.$ $\sin \theta$

$3.$ $\operatorname{cosec}(90^\circ - \theta)$ $c.$ $1$

$d.$ $\tan \theta$

Medium

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$1. \cos \theta$	$a. \frac{\cos \theta}{\sin \theta}$
$2. \tan \theta$	$b. \frac{1}{\csc \theta}$
$3. \cot \theta$	$c. \frac{1}{\sec \theta}$
$4. \sin \theta$	$d. \frac{1}{\cot \theta}$
	$e. \sin \theta \cdot \cos \theta$

Part $I$	Part $II$
$1.$ $\cos(90^\circ - \theta)$	$a.$ $\sec \theta$
$2.$ $\cot(90^\circ - \theta)$	$b.$ $\sin \theta$
$3.$ $\operatorname{cosec}(90^\circ - \theta)$	$c.$ $1$
	$d.$ $\tan \theta$

The value of $\sin^{2} 30^{\circ} - \tan 45^{\circ} + \cos^{2} 60^{\circ} - \cot 90^{\circ}$ is ........

Similar Questions

Which of the following pairs is correct for trigonometric inter-relationships? $1. \cos \theta$ $a. \frac{\cos \theta}{\sin \theta}$ $2. \tan \theta$ $b. \frac{1}{\csc \theta}$ $3. \cot \theta$ $c. \frac{1}{\sec \theta}$ $4. \sin \theta$ $d. \frac{1}{\cot \theta}$ $e. \sin \theta \cdot \cos \theta$

If $\sec 4A = \operatorname{cosec}(A - 20^\circ)$,where $4A$ is an acute angle,then the value of $A$ is $\ldots \ldots \ldots \ldots .$ (in $^\circ$)

If $\sin ^{2}(3 x+30^{\circ})+\cos ^{2}(2 x+45^{\circ})=1$,then $x = \dots$ (in $^{\circ}$)

If $\sin 5 \theta = \cos 5 \theta$,then the value of $\theta$ is ..........

Which of the following groups truly matches the data of Part $I$ with the data of Part $II$? Part $I$ Part $II$ $1.$ $\cos(90^\circ - \theta)$ $a.$ $\sec \theta$ $2.$ $\cot(90^\circ - \theta)$ $b.$ $\sin \theta$ $3.$ $\operatorname{cosec}(90^\circ - \theta)$ $c.$ $1$ $d.$ $\tan \theta$

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Which of the following groups truly matches the data of Part $I$ with the data of Part $II$?

Part $I$ Part $II$

$1.$ $\cos(90^\circ - \theta)$ $a.$ $\sec \theta$

$2.$ $\cot(90^\circ - \theta)$ $b.$ $\sin \theta$

$3.$ $\operatorname{cosec}(90^\circ - \theta)$ $c.$ $1$

$d.$ $\tan \theta$