sin 60^{circ} cdot cos 30^{circ} + cos 60^{ci | vedclass

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Question

(A) The given expression is $\sin 60^{\circ} \cdot \cos 30^{\circ} + \cos 60^{\circ} \cdot \sin 30^{\circ}$.We know the trigonometric values: $\sin 60

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$1$

Vedclass · Answer

(A) The given expression is $\sin 60^{\circ} \cdot \cos 30^{\circ} + \cos 60^{\circ} \cdot \sin 30^{\circ}$.We know the trigonometric values: $\sin 60^{\circ} = \frac{\sqrt{3}}{2}$,$\cos 30^{\circ} = \frac{\sqrt{3}}{2}$,$\cos 60^{\circ} = \frac{1}{2}$,and $\sin 30^{\circ} = \frac{1}{2}$.Substituting these values into the expression:$= (\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}) + (\frac{1}{2} \cdot \frac{1}{2})$$= \frac{3}{4} + \frac{1}{4}$$= \frac{4}{4} = 1$.Alternatively,using the identity $\sin(A + B) = \sin A \cos B + \cos A \sin B$,where $A = 60^{\circ}$ and $B = 30^{\circ}$:$= \sin(60^{\circ} + 30^{\circ}) = \sin 90^{\circ} = 1$.

$\sin 60^{\circ} \cdot \cos 30^{\circ} + \cos 60^{\circ} \cdot \sin 30^{\circ} = ..........$

Similar Questions

The value of the expression $\left[\operatorname{cosec}(75^{\circ}+\theta)-\sec(15^{\circ}-\theta)-\tan(55^{\circ}+\theta)+\cot(35^{\circ}-\theta)\right]$ is

Write 'True' or 'False' and justify your answer.
$\sqrt{(1-\cos^2 \theta) \sec^2 \theta} = \tan \theta$

$\frac{\sec \theta-1}{\sec \theta+1} = \ldots$

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$\frac{\sin 60^{\circ} + \cos 30^{\circ}}{1 + \sin 30^{\circ} + \cos 60^{\circ}} = \dots$

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