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Question: The value of \(\cos 15^{o} = \cos(45^{o} - 30^{o}) = \frac{\sqrt{3} + 1}{2\sqrt{2}}\), when \(\sin 1...

The value of cos⁡15o=cos⁡(45o−30o)=3+122\cos 15^{o} = \cos(45^{o} - 30^{o}) = \frac{\sqrt{3} + 1}{2\sqrt{2}}, when sin⁡15o.cos⁡15o=12(2sin⁡15ocos⁡15o)=12sin⁡30o=14\sin 15^{o}.\cos 15^{o} = \frac{1}{2}(2\sin 15^{o}\cos 15^{o}) = \frac{1}{2}\sin 30^{o} = \frac{1}{4} is

A

sin⁡15o.cos⁡75o=sin⁡15o.sin⁡15o=sin⁡215o\sin 15^{o}.\cos 75^{o} = \sin 15^{o}.\sin 15^{o} = \sin^{2}15^{o}

B

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

C

0

D

1

Answer

0

Explanation

Solution

cos⁡5π4−sin⁡5π4⇒−cos⁡π4+sin⁡π4⇒−12+12=0\cos\frac{5\pi}{4} - \sin\frac{5\pi}{4} \Rightarrow - \cos\frac{\pi}{4} + \sin\frac{\pi}{4} \Rightarrow - \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = 0.