Question2
Prove the following dentities
a)

Ask by Kelly Burgess. in South Africa

Mar 14,2025

Question

Question2 Prove the following dentities a) $$ \sin x / 1-\cos 2 x=1 / 2 \sin x $$

UpStudy AI · Accepted Answer

1. Start with the left-hand side:
   $$
   \frac{\sin x}{1-\cos 2x}
   $$

2. Recall the double-angle identity for cosine:
   $$
   \cos 2x = 1- 2\sin^2 x.
   $$
   Then,
   $$
   1-\cos 2x = 1 - (1-2\sin^2 x)= 2\sin^2 x.
   $$

3. Substitute $$1-\cos2x$$ in the original expression:
   $$
   \frac{\sin x}{1-\cos 2x} = \frac{\sin x}{2\sin^2 x}.
   $$

4. Cancel a factor of $$\sin x$$ (assuming $$\sin x\ne 0$$):
   $$
   \frac{\sin x}{2\sin^2 x} = \frac{1}{2\sin x}.
   $$

Thus, we have shown that:
$$
\frac{\sin x}{1-\cos 2x} = \frac{1}{2\sin x}.
$$
$$ \frac{\sin x}{1-\cos 2x} = \frac{1}{2\sin x} $$

Question2
Prove the following dentities
a)

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