adatic polynomial (6x-7x -3) and verify the relation between its zand

1.	adatic polynomial (6x-7x -3) and verify the relation between its zand coefficients.Prove that sin2 θ + cos2 θ = 1
Answer» Let theta = x 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.

adatic polynomial (6x-7x -3) and verify the relation between its zand coefficients.Prove that sin2 θ + cos2 θ = 1

Answer»

Let theta = x

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.