in proving trigonometric identities if sec theta - tan theta sin theta is equal to cos theta. what is the correct answer?

secØ - tanØsinØ = cosØ

LS (left side)
= 1/cosØ - (sinØ/cosØ)sinØ
= (1 - sin^2 Ø)/cosØ
= cos^2 Ø/cosØ
= cosØ
= RS

To determine if the given expression sec(theta) - tan(theta) sin(theta) is equal to cos(theta), we can start by simplifying the expression using trigonometric identities.

1. Recall the definitions of sec(theta), tan(theta), and sin(theta):
sec(theta) = 1/cos(theta)
tan(theta) = sin(theta)/cos(theta)

2. Substitute the values into the given expression:
sec(theta) - tan(theta) sin(theta) = (1/cos(theta)) - (sin(theta)/cos(theta)) * sin(theta)

3. Combine the two terms on the right-hand side:
sec(theta) - tan(theta) sin(theta) = (1 - sin^2(theta))/cos(theta)

4. Notice that 1 - sin^2(theta) is equal to cos^2(theta) due to the Pythagorean identity:
sec(theta) - tan(theta) sin(theta) = cos^2(theta)/cos(theta)

5. Simplify further by canceling out the common factor of cos(theta) in the numerator and denominator:
sec(theta) - tan(theta) sin(theta) = cos(theta)

Therefore, the given expression sec(theta) - tan(theta) sin(theta) is indeed equal to cos(theta).