Question

(1-cos2a)tg2a+1-tg2a​

Answer 1

Ответ:

-sin2a +1

Объяснение:

(1-cos2a)tg2a+1-tg2a=

= tg2a*1-tg2a*cos2a+1-tg2a=

= tg2a-(sin2a/cos2a)*cos2a+1-tg2a=

= tg2a-sin2a+1-tg2a=

= (tg2a-tg2a) -sin2a +1=

= 0 -sin2a +1 = -sin2a +1

Answer 2

To simplify the expression (1 - cos^2(a)) * tan^2(a) + 1 - tan^2(a), you can use trigonometric identities.

Start by using the Pythagorean identity for tangent:

tan^2(a) = sec^2(a) - 1

Now, substitute this identity into the expression:

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

Next, distribute the terms:

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

Now, simplify each part of the expression:

1. (sec^2(a) - cos^2(a)) can be simplified using the Pythagorean identity for sine: sec^2(a) - cos^2(a) = 1.
2. 1 - sec^2(a) + 1 simplifies to -sec^2(a).

So, the expression becomes:

1 * (sec^2(a) - 1) - sec^2(a) + 1

Now, distribute the 1:

sec^2(a) - 1 - sec^2(a) + 1

Now, you can see that the terms sec^2(a) and -sec^2(a) cancel out, and you are left with:

-1

So, the simplified expression is -1.