Is (csc(θ))/(1+tan(θ))=cot^2(θ) ?

The answer to whether (csc(θ))/(1+tan(θ))=cot^2(θ) is False

prove (csc(θ))/(1+tan(θ))=cot^2(θ)

prove

\frac{csc ( θ )}{1 + tan ( θ )} = cot^{2} (θ)

False

Solution steps

\frac{csc ( θ )}{1 + tan ( θ )} = cot^{2} (θ)

Show that the two sides are not equal

For

\frac{csc ( θ )}{1 + tan ( θ )} = cot^{2} (θ)

plug in

θ = 1

\frac{csc ( 1 )}{1 + tan ( 1 )} = 0.46468 \dots

\frac{csc ( 1 )}{1 + tan ( 1 )}

Refine to a decimal form

= 0.46468 \dots

cot^{2} (1) = 0.41228 \dots

cot^{2} (1)

Refine to a decimal form

= 0.41228 \dots

The two sides are not equal

\Rightarrow False

p ro v e - \frac{- 1 + sin ^{2} ( θ )}{sin ^{2} ( θ )} = cot^{2} (θ)

p ro v e cos (2 A + A) = - 3 cos (A) + 4 cos^{3} (A)

p ro v e (sin^{2} (x) + cos^{2} (x))^{3} = 1^{3}

p ro v e cos (- x) \cdot cot (x) + sin (x) = csc (x)

p ro v e \frac{0}{sin ( θ )} = \frac{1}{sin ( θ )} + 3

Is (csc(θ))/(1+tan(θ))=cot^2(θ) ?
The answer to whether (csc(θ))/(1+tan(θ))=cot^2(θ) is False