Simplify: 2θ - 1/ 2θ

Correct Answer is : −tan⁡θ- θ−tanθ

Correct Answer is : −tan⁡θ- θ−tanθ

Test Index

WAEC Further Mathematics 2012 Paper

Question : 2

Total: 40

Simplify:

\frac{\cos 2\theta - 1}{\sin 2\theta}

Solution:

Concept:

Use the double-angle identities for

\cos 2\theta

and

\sin 2\theta

to simplify the fraction.

Explanation:

Recall:

\cos 2\theta = 1 - 2\sin^2 \theta

Also recall:

\sin 2\theta = 2\sin \theta \cos \theta

Substitute these into the given expression.

\frac{\cos 2\theta - 1}{\sin 2\theta} = \frac{(1 - 2\sin^2 \theta) - 1}{2\sin \theta \cos \theta}

Simplify the numerator:

1 - 2\sin^2 \theta - 1 = -2\sin^2 \theta

So the expression becomes

\frac{-2\sin^2 \theta}{2\sin \theta \cos \theta}

Cancel the common factor

2\sin \theta

\frac{-\sin \theta}{\cos \theta}

Since

\frac{\sin \theta}{\cos \theta} = \tan \theta

, the result is

-\tan \theta

Answer:

-\tan \theta

, which is option A.

Go to Question:

Prev Question

Next Question