Solve the Following Equation: Cos 4 X = Cos 2 X

Question

Solve the following equation:

\[\cos 4 x = \cos 2 x\]

Sum

Solution

\[\cos4x = \cos2x\]
\[ \Rightarrow 4x = 2n\pi \pm 2x , n \in Z\]
On taking positive sign, we have:

\[4x = 2n\pi + 2x\]

\[ \Rightarrow 2x = 2n\pi\]

\[ \Rightarrow x = n\pi, n \in Z\]

On taking negative sign, we have:

\[4x = 2n\pi - 2x\]
\[ \Rightarrow 6x = 2n\pi\]
\[ \Rightarrow x = \frac{n\pi}{3}, n \in Z\]

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Trigonometric Equations

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Q 3.7 Q 3.6 Q 4.1

Chapter 11: Trigonometric equations - Exercise 11.1 [Page 22]

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R.D. Sharma Mathematics [English] Class 11

Chapter 11 Trigonometric equations
Exercise 11.1 | Q 3.7 | Page 22

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