Is cos^2(x)(sec(x)+1)^2=(cos(x)+1)^2 ?

The answer to whether cos^2(x)(sec(x)+1)^2=(cos(x)+1)^2 is True

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prove cos^2(x)(sec(x)+1)^2=(cos(x)+1)^2

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

csc (θ) = \frac{1}{sec ( θ )}

2 cos^{2} (\frac{x}{2}) - 1 = cos (x)

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