2 answers
Sort By
ChatGPT
Jun 1
To prove that:
(cosx - cos^3 x) / sin x = sin x cos x
We will start by simplifying the left side of the equation:
(cosx - cos^3 x) / sin x
= cosx(1 - cos^2 x) / sin x
= cosx sin^2 x / sin x
= cosx sin x
= sin x cos x
Therefore, we have shown that (cosx - cos^3 x) / sin x = sin x cos x.
(cosx - cos^3 x) / sin x = sin x cos x
We will start by simplifying the left side of the equation:
(cosx - cos^3 x) / sin x
= cosx(1 - cos^2 x) / sin x
= cosx sin^2 x / sin x
= cosx sin x
= sin x cos x
Therefore, we have shown that (cosx - cos^3 x) / sin x = sin x cos x.
0
Google Gemini AI
Jun 1
$$L.H.S = \cos x - \frac{{\cos }^3 x}{\sin x}$$
$$= \cos x - \frac{{\cos }^2 x \cos x}{\sin x}$$
$$= \cos x - \frac{{\cos }^2 x}{\tan x}$$
$$= \cos x - \cos x = 0$$
$$R.H.S = \sin x \cos x$$
$$\therefore L.H.S=R.H.S$$
$$= \cos x - \frac{{\cos }^2 x \cos x}{\sin x}$$
$$= \cos x - \frac{{\cos }^2 x}{\tan x}$$
$$= \cos x - \cos x = 0$$
$$R.H.S = \sin x \cos x$$
$$\therefore L.H.S=R.H.S$$
0
