Find out the value of sec 15

We have to find out the value of sec 15°

Solution:

We know that sec function is the inverse function of cos function, first find the value of cos 15°.

So, Cos 15°= cos(45°-30°)Now, take the values a = 45°and b = 30°

By using the formula, Cos (a-b) = cos a cos b + sin a sin b

So, it becomes Cos 15° = cos 45° cos 30° +sin 45° sin 30°

\(\cos 15^{\circ}= \frac{1}{\sqrt{2}}\frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\frac{1}{2}\\ \cos 15^{\circ}= \frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2\sqrt{2}}\\ \cos 15^{\circ}= \frac{\sqrt{3}+1}{2\sqrt{2}}\)

Therefore, sec 15° = 1/cos 15° \(Sec 15^{\circ} = \frac{1}{\frac{\sqrt{3}+1}{2\sqrt{2}}}\)

Therefore, \(sec 15^{\circ}=\frac{2\sqrt{2}}{\sqrt{3}+1}\)

Answer

Therefore, \(sec 15^{\circ}=\frac{2\sqrt{2}}{\sqrt{3}+1}\)

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