Is (cos(θ)cot(θ))/(1-sin(θ))-1=sin(θ) ?

The answer to whether (cos(θ)cot(θ))/(1-sin(θ))-1=sin(θ) is False

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prove (cos(θ)cot(θ))/(1-sin(θ))-1=sin(θ)

prove

\frac{cos ( θ ) cot ( θ )}{1 - sin ( θ )} - 1 = sin (θ)

False

Solution steps

\frac{cos ( θ ) cot ( θ )}{1 - sin ( θ )} - 1 = sin (θ)

Show that the two sides are not equal

For

\frac{cos ( θ ) cot ( θ )}{1 - sin ( θ )} - 1 = sin (θ)

plug in

θ = 1

\frac{cos ( 1 ) cot ( 1 )}{1 - sin ( 1 )} - 1 = 1.18839 \dots

\frac{cos ( 1 ) cot ( 1 )}{1 - sin ( 1 )} - 1

Refine to a decimal form

= 1.18839 \dots

sin (1) = 0.84147 \dots

sin (1)

Refine to a decimal form

= 0.84147 \dots

The two sides are not equal

\Rightarrow False

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

2 tan (x) = \frac{2 sin ( x )}{cos ( x )}

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

sin (t) cos (t) = 1

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

Is (cos(θ)cot(θ))/(1-sin(θ))-1=sin(θ) ?
The answer to whether (cos(θ)cot(θ))/(1-sin(θ))-1=sin(θ) is False