sin ^{2} 1^{circ} + sin ^{2} 3^{circ} + sin ^ | vedclass

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(C) We are given the expression: $\sin ^{2} 1^{\circ} + \sin ^{2} 3^{\circ} + \sin ^{2} 87^{\circ} + \sin ^{2} 89^{\circ}$.Using the trigonometric ide

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(C) We are given the expression: $\sin ^{2} 1^{\circ} + \sin ^{2} 3^{\circ} + \sin ^{2} 87^{\circ} + \sin ^{2} 89^{\circ}$.Using the trigonometric identity $\sin(90^{\circ} - 	heta) = \cos 	heta$,we can rewrite the terms:$\sin ^{2} 87^{\circ} = \sin ^{2}(90^{\circ} - 3^{\circ}) = \cos ^{2} 3^{\circ}$$\sin ^{2} 89^{\circ} = \sin ^{2}(90^{\circ} - 1^{\circ}) = \cos ^{2} 1^{\circ}$Substituting these into the original expression:$= \sin ^{2} 1^{\circ} + \sin ^{2} 3^{\circ} + \cos ^{2} 3^{\circ} + \cos ^{2} 1^{\circ}$Grouping the terms with the same angle:$= (\sin ^{2} 1^{\circ} + \cos ^{2} 1^{\circ}) + (\sin ^{2} 3^{\circ} + \cos ^{2} 3^{\circ})$Using the identity $\sin ^{2} 	heta + \cos ^{2} 	heta = 1$:$= 1 + 1 = 2$.

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

$\sin ^{2} 1^{\circ} + \sin ^{2} 3^{\circ} + \sin ^{2} 87^{\circ} + \sin ^{2} 89^{\circ} = \ldots$

Similar Questions

$2A$ is the measure of an acute angle and $\sec 2A = \operatorname{cosec}(A - 42^\circ)$,then the value of $A$ is $\ldots \ldots \ldots \ldots$ (in $^\circ$)

If $a \sin \theta + b \cos \theta = c$,then prove that $a \cos \theta - b \sin \theta = \pm \sqrt{a^2 + b^2 - c^2}$,given $a^2 + b^2 \geq c^2$.

$\tan ^{2} \theta - \sec ^{2} \theta = \ldots \ldots \ldots$

Which of the following is true for some $\theta$ (where,$0 < \theta < 90^{\circ}$)?

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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