Is (sin(2x))^2+(cos(2x))^2=1 ?

The answer to whether (sin(2x))^2+(cos(2x))^2=1 is True

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prove (sin(2x))^2+(cos(2x))^2=1

prove

(sin (2 x))^{2} + (cos (2 x))^{2} = 1

True

Solution steps

(sin (2 x))^{2} + (cos (2 x))^{2} = 1

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

\Rightarrow True

1 - sin^{5} (x) = cos^{2} (x)

cot (\frac{π}{2} - θ) cot (θ) = 1

cos (\frac{x}{2}) (1 - cos (x)) = sin (\frac{x}{2}) sin (x)

\frac{csc ( x ) - cot ( x )}{sec ( x ) - 1} = csc (x)

\frac{csc ^{2} ( t )}{cot ( t )} = tan (t) + cot (t)

Is (sin(2x))^2+(cos(2x))^2=1 ?
The answer to whether (sin(2x))^2+(cos(2x))^2=1 is True