Question

Cos3 theta ÷ 2cos2 theta-1

Answer 1

Answer:

COS θ

Step-by-step explanation:

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Answer 2

Answer:

$cos\theta$ is the  required value of $\frac{Cos 3\theta}{2cos2\theta - 1}$ .

Step-by-step explanation:

Explanation:

Given , $\frac{Cos 3\theta}{2cos2\theta - 1}$

To solve the given question we use the  formula ,

$Cos 3 \theta = 4cos ^3\theta - 3 cos\theta$ and $cos2\theta = 2cos^2-1$ .

Step 1:

From the question we have  $\frac{Cos 3\theta}{2cos2\theta - 1}$  ,

$\frac{Cos 3\theta}{2cos2\theta - 1}$ this can be written as $\frac{4cos ^3\theta - 3 cos\theta}{2cos2\theta - 1}$       [∴$Cos 3 \theta = 4cos ^3\theta - 3 cos\theta$]

⇒$\frac{4cos ^3\theta - 3 cos\theta}{2cos2\theta - 1}$ =  $\frac{4cos ^3\theta - 3 cos\theta}{2(2cos^2\theta -1) - 1}$                      [∴$cos2\theta = 2cos^2-1$]

⇒$\frac{4cos ^3\theta - 3 cos\theta}{4cos^2\theta -3}$

Take common $cos \theta$ from numerator

⇒$\frac{cos\theta(4cos ^2\theta - 3 )}{4cos^2\theta -3}$ = $cos\theta$ .

Final answer :

Hence . the value of $\frac{Cos 3\theta}{2cos2\theta - 1}$ is $cos\theta$ .

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