Is (cos(θ)-sin(θ))^2=1 ?

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

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prove (cos(θ)-sin(θ))^2=1

prove

(cos (θ) - sin (θ))^{2} = 1

False

Solution steps

(cos (θ) - sin (θ))^{2} = 1

Show that the two sides are not equal

For

(cos (θ) - sin (θ))^{2} = 1

plug in

θ = 1

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

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

Refine to a decimal form

= 0.09070 \dots

The two sides are not equal

\Rightarrow False

cos (x) = 1 = cos (0) = 1

(tan (x) + 1) (tan (x) - 1) = sec^{2} (x) - 2

\frac{1}{csc ( x ) + 1} = \frac{1}{sin ( x ) + 1}

tan (θ) + 1 = \frac{sin ( θ )}{cos ( θ )} + 1

(1 + tan^{2} (α)) cos^{2} (α) = 1