Question

(sin^2a-cos^2a sin^2)/cos^2a sin^2a

Answer 1

Ответ:

Объяснение:

[ sin^2a*(1-cos^2a) ] / cos^2a*sin^2a = sin^2a*sin^2a/sin^2a*cos^2a=

=sin^2a/cos^2a=tg^2a

Answer 2

Let's simplify the expression step by step:

(sin^2(a) - cos^2(a)) / (cos^2(a) * sin^2(a))

Step 1: Apply trigonometric identities.

Recall the Pythagorean identity: sin^2(a) + cos^2(a) = 1

Now, rearrange the identity to isolate sin^2(a): sin^2(a) = 1 - cos^2(a)

Step 2: Substitute sin^2(a) in the expression.

(sin^2(a) - cos^2(a)) / (cos^2(a) * sin^2(a)) = (1 - cos^2(a) - cos^2(a)) / (cos^2(a) * (1 - cos^2(a)))

Step 3: Combine like terms.

= (1 - 2cos^2(a)) / (cos^2(a) - cos^4(a))

Step 4: Factor out a common term in the numerator.

= 1 / (cos^2(a) - cos^4(a)) - 2cos^2(a) / (cos^2(a) - cos^4(a))

Now, we have simplified the expression as much as possible. It can be further simplified if there are any additional instructions or if the expression is meant to be evaluated for a specific value of 'a'. If you have further instructions or a specific value for 'a', please provide them, and I'll be happy to help you further.