Question

Срочно! tg^2a×ctg^2a-cos^2a

Answer 1

Tg^2a*ctg^2a-cos^2a=1-cos^2a=sin^2a

Answer 2

To simplify the given expression, we'll use trigonometric identities. Let's break it down step by step:

Given expression: tg^2(a) × ctg^2(a) - cos^2(a)

1. Recall the basic trigonometric identity: tan(a) = sin(a) / cos(a)
2. The cotangent (ctg) of an angle is the reciprocal of its tangent: ctg(a) = 1 / tan(a) = cos(a) / sin(a)

Using the above identities, let's rewrite the expression:

tg^2(a) × ctg^2(a) = (sin^2(a) / cos^2(a)) × (cos^2(a) / sin^2(a))

The sin^2(a) and cos^2(a) terms in the numerator and denominator cancel each other out, leaving us with:

tg^2(a) × ctg^2(a) = 1

Now the expression becomes:

1 - cos^2(a)

Finally, we can use the Pythagorean identity for trigonometric functions:

sin^2(a) + cos^2(a) = 1

Rearranging the terms, we get:

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

Substitute this into the expression:

1 - cos^2(a) = 1 - (1 - sin^2(a)) = 1 - 1 + sin^2(a) = sin^2(a)

So, the simplified expression is: sin^2(a)