Question

1/1+tg^2а решение sin2a?

Answer 1

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Answer 2

To solve for sin(2a), let's first simplify the expression 1/(1 + tan^2(a)):

We know that tan^2(a) + 1 = sec^2(a) (this is a trigonometric identity). Therefore:

1/(1 + tan^2(a)) = 1/(sec^2(a)) = cos^2(a).

Now, we can use the double angle formula for sine to find sin(2a):

sin(2a) = 2sin(a)cos(a).

Since we already have cos^2(a) from the simplification earlier, we can find sin(a) by using the Pythagorean identity:

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

Therefore:

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

Now, we can substitute sin^2(a) into the double angle formula:

sin(2a) = 2sin(a)cos(a) = 2√(1 - cos^2(a)) * cos(a).

This is the expression for sin(2a) in terms of cos(a), and we already determined that cos^2(a) = 1/(1 + tan^2(a)). So, the final answer for sin(2a) is:

sin(2a) = 2√(1 - 1/(1 + tan^2(a))) * (1/√(1 + tan^2(a))).