Question : $\cos 2 \theta=$________.
Option 1: $1-2 \cos^2 \theta$
Option 2: $2 \cos^2 \theta-1$
Option 3: $2 \sin^2 \theta-1$
Option 4: $1-\sin^2 \theta$

Question

Question : What is the value of $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}+\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}$?
Option 1: $\frac{1}{\left(\sin ^2 \theta-\cos ^2 \theta\right)}$
Option 2: $2\left(\sin ^2 \theta-\cos ^2 \theta\right)$
Option 3: $\frac{2}{\left(\sin ^2 \theta-\cos ^2 \theta\right)}$
Option 4: $\sin ^2 \theta-\cos ^2 \theta$

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Answer 1

Correct Answer: $2 \cos^2 \theta-1$

Solution : $\cos2\theta = \cos^2\theta-\sin^2\theta$
$= \cos^2\theta-(1-\cos^2\theta)$
$= 2\cos^2\theta-1$
Hence, the correct answer is $2\cos^2\theta-1$.

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Question : $\cos 2 \theta=$________.Option 1: $1-2 \cos^2 \theta$Option 2: $2 \cos^2 \theta-1$Option 3: $2 \sin^2 \theta-1$Option 4: $1-\sin^2 \theta$

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Question : $\cos 2 \theta=$________.
Option 1: $1-2 \cos^2 \theta$
Option 2: $2 \cos^2 \theta-1$
Option 3: $2 \sin^2 \theta-1$
Option 4: $1-\sin^2 \theta$