The value of 15^{}- 15^{} is ......

Correct Answer is : 12{1}{{2}}21

Correct Answer is : 12{1}{{2}}21

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MHTCET 20 Apr 2026 Shift 1 Paper

Question : 105 of 150

Marks: +1, -0

The value of

\cos 15^{\circ}-\sin 15^{\circ}

is ......

Solution:

Concept:

The expression

\cos 15^{\circ}-\sin 15^{\circ}

can be simplified using the standard identity

\cos x-\sin x=\sqrt{2}\cos(x+45^{\circ})

Explanation:

Use the identity

\cos x-\sin x=\sqrt{2}\cos(x+45^{\circ})

Put

x=15^{\circ}

Then,

\cos 15^{\circ}-\sin 15^{\circ}=\sqrt{2}\cos(15^{\circ}+45^{\circ})

This becomes

\sqrt{2}\cos 60^{\circ}

We know

\cos 60^{\circ}=\frac{1}{2}

Therefore,

\sqrt{2}\times \frac{1}{2}=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}

Answer:

\frac{1}{\sqrt{2}}

Hence, the correct option is C.

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