Is (cot(x)+1)^2=csc^2(x)+2cot(x) ?

The answer to whether (cot(x)+1)^2=csc^2(x)+2cot(x) is True

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prove (cot(x)+1)^2=csc^2(x)+2cot(x)

prove

(cot (x) + 1)^{2} = csc^{2} (x) + 2 cot (x)

True

Solution steps

(cot (x) + 1)^{2} = csc^{2} (x) + 2 cot (x)

Manipulating left side

(cot (x) + 1)^{2}

Expand

(1 + cot (x))^{2} : 1 + 2 cot (x) + cot^{2} (x)

= 1 + cot^{2} (x) + 2 cot (x)

Manipulating right side

csc^{2} (x) + 2 cot (x)

Rewrite using trig identities

= 1 + cot^{2} (x) + 2 cot (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) = - cos (θ + \frac{π}{2})

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

cos^{2} (x) (sec (x) + 1)^{2} = (cos (x) + 1)^{2}

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

\frac{cos ( u )}{1 + tan ( u )} - \frac{sin ( u )}{1 + cot ( u )} = cos (u) - sin (u)

Is (cot(x)+1)^2=csc^2(x)+2cot(x) ?
The answer to whether (cot(x)+1)^2=csc^2(x)+2cot(x) is True