Question

Prove that: ..................................​

Answer 1

Explanation:

`\displaystyle\\cos^2\alpha +cos^2\alpha cot^2\alpha =\\\\cos^2\alpha (1+cot^2\alpha )=\\\\cos^2\alpha (1+(cos^2\alpha )/(sin^2\alpha ) )=\\\\cos^2\alpha ((sin^2\alpha +cos^2\alpha )/(sin^2\alpha ) )=\\\\cos^2\alpha ((1)/(sin^2\alpha ) )=\\\\(cos^2\alpha )/(sin^2\alpha )=\\\\cot^2\alpha`

Answer 2

Starting with the left side of the equation:

cos² a + cos² a cot² a

We can simplify the left side by using the identity cot² a = 1/tan² a

cos² a + cos² a * (1/tan² a)

We can simplify further by using the identity tan² a = (1/cos² a) - 1

cos² a + (1 - cos² a)

Now we have the left side of the equation equals to 1 which is the right side of the equation.

Explanation:

see above