Show that the two ratios below are equal for any acute angle .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Show that the two ratios below are equal for any acute angle

\theta

. (i) Compare

\dfrac{1-\cos\theta}{\sin\theta}

and

\dfrac{\sin\theta}{1+\cos\theta}

, and prove that they are equal. (ii) Evaluate the common value of these ratios when

\theta=45^\circ