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Question: Period of \(\cos\frac{x}{3}\) is....

Period of cos⁡x3\cos\frac{x}{3} is.

A

6π6\pi

B

12π12\pi

C

cot⁡3x\cot 3x

D

π3\frac{\pi}{3}

Answer

π3\frac{\pi}{3}

Explanation

Solution

Period of =sin⁡126osin⁡(18o)=5+15−1= \frac{\sin 126^{o}}{\sin(18^{o})} = \frac{\sqrt{5} + 1}{\sqrt{5} - 1} is cos⁡C=π3⇒a2+b2−c2=ab\cos C = \frac{\pi}{3} \Rightarrow a^{2} + b^{2} - c^{2} = ab and period of b2+bc+a2+ac=ab+ac+bc+c2b^{2} + bc + a^{2} + ac = ab + ac + bc + c^{2} is b(b+c)+a(a+c)=(a+c)(b+c)b(b + c) + a(a + c) = (a + c)(b + c). Hence period of expression is (a+c) (b+c)(a + c)\ (b + c) (L.C.M.).