Question

prove that sin^2A+cos^2A=1​

Answer 1

Answer:

F(x) = sin^2(x) + cos^2(x)

f '(x) = 2 sin(x) cos(x) + 2 cos(x) (-sin(x))

= 2 sin(x) cos(x) - 2 cos(x) sin(x)

= 0

Since the derivative is zero everywhere the function must be a constant.

Take f(0) = sin^2(0) + cos^2(0) = 0 + 1 = 1

So

sin^2(x) + cos^2(x) = 1 everywhere.

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