(B) We use the trigonometric identity: $\cos ^{2} A - \sin ^{2} B = \cos(A+B) \cdot \cos(A-B)$.Here,$A = 45^{\circ}$ and $B = 15^{\circ}$.Substituting

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(B) We use the trigonometric identity: $\cos ^{2} A - \sin ^{2} B = \cos(A+B) \cdot \cos(A-B)$.Here,$A = 45^{\circ}$ and $B = 15^{\circ}$.Substituting these values into the identity:$\cos ^{2} 45^{\circ} - \sin ^{2} 15^{\circ} = \cos(45^{\circ} + 15^{\circ}) \cdot \cos(45^{\circ} - 15^{\circ})$$= \cos(60^{\circ}) \cdot \cos(30^{\circ})$$= \frac{1}{2} \times \frac{\sqrt{3}}{2}$$= \frac{\sqrt{3}}{4}$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Trigonometrical ratios of sum and difference of two and three angles

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The value of $\cos ^{2} 45^{\circ}-\sin ^{2} 15^{\circ}$ is

KCET 2017 All KCET

A
$\frac{\sqrt{3}}{2}$
B
$\frac{\sqrt{3}}{4}$
C
$\frac{\sqrt{3}+1}{2 \sqrt{2}}$
D
$\frac{\sqrt{3}-1}{2 \sqrt{2}}$

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Trigonometrical Ratios, Functions and Identities

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Trigonometrical ratios of sum and difference of two and three angles

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