Test Index

Trigonometry Practice Test 1

© examsnet.com

Question : 15 of 40

Marks: +1, -0

If

\frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=4

, then what is the value of θ, where

0 \leq \theta \leq \frac{\pi}{2}?

30°
45°
60°
90°
None of these

Solution: 👈: Video Solution

Concept:

Combine the two fractions and use the identity

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

.

Explanation:

Given:

\frac{\sin\theta}{1+\cos\theta}+\frac{1+\cos\theta}{\sin\theta}=4

.

Taking LCM:

\frac{\sin^2\theta+(1+\cos\theta)^2}{(1+\cos\theta)\sin\theta}=4

.

Expand the numerator:

\sin^2\theta+1+2\cos\theta+\cos^2\theta

.

Since

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

, the numerator becomes

2+2\cos\theta=2(1+\cos\theta)

.

So,

\frac{2(1+\cos\theta)}{(1+\cos\theta)\sin\theta}=4

.

Cancel

1+\cos\theta

:

\frac{2}{\sin\theta}=4

.

Thus,

\sin\theta=\frac{1}{2}

.

For

0\le\theta\le\frac{\pi}{2}

,

\theta=30^\circ

.

Answer:

\theta=30^\circ

(or

\frac{\pi}{6}

).

© examsnet.com

Go to Question:

Prev Question

Next Question