SATHEE: Trigonometrical Equations 1 Question 28

Trigonometrical Equations 1 Question 28

28. Find the values of $x (- π, π)$ which satisfy the equation $2^{1 + | \cos x | + | \cos^{2} x | + \dots} = 4$

(1984, 2M)

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Answer:

Correct Answer: 28. $\pm \frac{π}{3}, \pm \frac{2 π}{3}$

Solution:

Given, $2^{1 + | \cos x | + | \cos^{2} x | + | \cos^{3} x | + \dots .} = 2^{2}$

$\begin{array}{ll} \Rightarrow & 2^{\frac{1}{1 - | \cos x |}} = 2^{2} \\ \Rightarrow & \frac{1}{1 - | \cos x |} = 2 \end{array}$

$\begin{array}{ll} \Rightarrow & | \cos x | = \frac{1}{2} \\ \Rightarrow & \cos x = \pm \frac{1}{2} \\ ∴ & x = \frac{π}{3}, \frac{2 π}{3}, - \frac{π}{3}, - \frac{2 π}{3} [∵ x \in (- π, π)] \end{array}$

Thus, the solution set is $\pm \frac{π}{3}, \pm \frac{2 π}{3}$ .

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Trigonometrical Equations 1 Question 28

28. Find the values of x(−π,π) which satisfy the equation 21+|cos⁡x|+|cos2⁡x|+…=4

Answer:

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28. Find the values of $x (- π, π)$ which satisfy the equation $2^{1 + | \cos x | + | \cos^{2} x | + \dots} = 4$