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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

cos^{2} (1) - sin^{2} (1) = - 0.41614 \dots

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

Refine to a decimal form

= - 0.41614 \dots

1 + 2 sin^{2} (1) = 2.41614 \dots

1 + 2 sin^{2} (1)

Refine to a decimal form

= 2.41614 \dots

The two sides are not equal

\Rightarrow False

cot (θ) csc (θ) sec (θ) = csc^{2} (θ)

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

4 sin (x) cos (x) cos (2 x) = sin (4 x)

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

- 2 tan^{2} (0) = 2 tan (0)

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