Is (cos(x)-sin(x))^2=sec^2(x)-2tan(x) ?

The answer to whether (cos(x)-sin(x))^2=sec^2(x)-2tan(x) is False

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prove (cos(x)-sin(x))^2=sec^2(x)-2tan(x)

prove

(cos (x) - sin (x))^{2} = sec^{2} (x) - 2 tan (x)

False

Solution steps

(cos (x) - sin (x))^{2} = sec^{2} (x) - 2 tan (x)

Show that the two sides are not equal

For

(cos (x) - sin (x))^{2} = sec^{2} (x) - 2 tan (x)

plug in

x = 1

(cos (1) - sin (1))^{2} = 0.09070 \dots

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

Refine to a decimal form

= 0.09070 \dots

sec^{2} (1) - 2 tan (1) = 0.31070 \dots

sec^{2} (1) - 2 tan (1)

Refine to a decimal form

= 0.31070 \dots

The two sides are not equal

\Rightarrow False

\frac{2 sec ^{2} ( x ) - 2 tan ^{2} ( x )}{csc ( x )} = sin (2 x) sec (x)

sin^{2} (θ) - 2 = - 1 - cos^{2} (θ)

sin (2 α) = 2 sin (α) cos (α)

cos (θ + π) = - cos (θ)

\frac{sec ^{2} ( θ ) - 1}{sin ( θ )} = tan (θ) sec (θ)

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