Prove that sin2a + cos2a = 1
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13
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.
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.
Answered by
3
Answer:
Step-by-step explanation:
Sin2a+cos2a+1
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