Please give me answer prove that, (sec {}^(2)a - 1) \cos {}^2a = \sin {}^(2) a answer please ​

Question

Please give me answer

prove that,

`(sec {}^(2)a - 1) \cos {}^2a = \sin {}^(2) a`
answer please
​

Answer 1

To prove the identity (sec²α - 1)cos²α = sin²α, we will manipulate the left-hand side (LHS) of the equation and show that it simplifies to the right-hand side (RHS). Here's the step-by-step proof:

Starting with the LHS:

(sec²α - 1)cos²α

We know that sec²α = 1/cos²α. Substituting this into the LHS, we get:

(1/cos²α - 1)cos²α

Now, we can simplify further:

1/cos²α * cos²α - 1 * cos²α

= 1 - cos²α

Using the trigonometric identity sin²α + cos²α = 1, we can substitute 1 - cos²α as sin²α:

= sin²α

Thus, we have shown that (sec²α - 1)cos²α simplifies to sin²α, which proves the given identity.

Therefore, (sec²α - 1)cos²α = sin²α.