Question

(sec

2
A−1)cos
2
A=sin
2
A

a) True
b) False
c) Cannot be determined
d) Depends on the value of A

Answer 1

The equation (sec^2 A - 1)cos^2 A = sin^2 A is true due to the application of trigonometric identities such as sec^2 A = 1 + tan^2 A and tan^2 A = sin^2 A / cos^2 A.

Step-by-step explanation:

The question asks if the equation (sec^2 A - 1)cos^2 A = sin^2 A is always true, false, cannot be determined, or depends on the value of A. To solve this, we can use trigonometric identities. The identity sec^2 A = 1 + tan^2 A allows us to rewrite the left-hand side of the equation as (tan^2 A)cos^2 A. Using another identity, tan A = sin A / cos A, we can express tan^2 A as (sin^2 A / cos^2 A). Substituting this into the equation, we get ((sin^2 A / cos^2 A) * cos^2 A) = sin^2 A, which simplifies to sin^2 A = sin^2 A. This shows that the original equation is indeed true regardless of the value of A, as long as A is within the domain of the trigonometric functions involved.