Question

Tg^2а-sin^2 а-tg^2 а*sin^2а

Answer 1

Упростить.

$tg^2a-sin^2a-tg^2a\cdot sin^2a=tg^2a(1-sin^2a)-sin^2a=tg^2a\cdot cos^2a-sin^2a=\\\\\\=\dfrac{sin^2a}{cos^2a}\cdot cos^2a-sin^2a=sin^2a-sin^2a=0$

Answer 2

It looks like you've provided an expression involving trigonometric functions. Let's break down and simplify the expression step by step:

Given expression:

tg^2(a) - sin^2(a) - tg^2(a) * sin^2(a)

First, let's work on simplifying this expression:

1. Recall the trigonometric identity: tan^2(x) = 1 - cos^2(x).

So, we can rewrite the first and third terms:

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

Now, our expression becomes:

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

2. Distribute the sin^2(a) term to both the first and last expressions:

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

3. Expand the last term by distributing the sin^2(a):

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

4. Combine like terms:

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

Now, using the Pythagorean identity sin^2(a) + cos^2(a) = 1, we can simplify further:

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

0 - sin^2(a) + cos^2(a) * sin^2(a)

Now, we have simplified the given expression to:

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

So, the simplified expression is -cos^2(a) * sin^2(a).