Question

Tg^2x-sin^2x=tg^2x×sin^2x

Answer 1

Так как в условии вы не указали, что нужно сделать (решить уравнение, доказать), то смотрите 2 решения.

Answer 2

I hope this helps you

Answer 3

To solve the trigonometric equation, we can use trigonometric identities and algebraic manipulation. Let's simplify the given equation step by step:

Starting with the equation:

tg^2(x) - sin^2(x) = tg^2(x) × sin^2(x)

We can use the identity: tan^2(x) = 1 - cos^2(x)

Rewrite the equation using this identity:

(1 - cos^2(x)) - sin^2(x) = (1 - cos^2(x)) × sin^2(x)

Now, we can simplify further:

1 - cos^2(x) - sin^2(x) = sin^2(x) - cos^2(x) × sin^2(x)

Recognize that sin^2(x) - cos^2(x) is the same as -cos^2(x) + sin^2(x):

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

Now, move all the terms to one side of the equation:

1 - cos^2(x) - sin^2(x) + cos^2(x) - sin^2(x) = 0

Combine like terms:

1 - 2cos^2(x) - 2sin^2(x) = 0

Now, use the Pythagorean identity: sin^2(x) + cos^2(x) = 1

Substitute this into the equation:

1 - 2cos^2(x) - 2(1 - cos^2(x)) = 0

Now, distribute the -2:

1 - 2cos^2(x) - 2 + 2cos^2(x) = 0

The -2cos^2(x) and 2cos^2(x) cancel each other out:

1 - 2 = 0

Now we have:

-1 = 0

The equation -1 = 0 is not true for any value of x. Thus, there is no solution to the original equation tg^2(x) - sin^2(x) = tg^2(x) × sin^2(x) for real values of x.