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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

sin^{2} (1) + cos (1^{2}) = 1.24837 \dots

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

Refine to a decimal form

= 1.24837 \dots

The two sides are not equal

\Rightarrow False

\frac{cos ( u )}{1 + tan ( u )} - \frac{sin ( u )}{1 + cot ( u )} = cos (u) - sin (u)

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

csc (θ) = \frac{1}{sec ( θ )}

cot (2 x) + tan (x) = csc (2 x)

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