Is tan^2(x+c)+1-(tan(x+c))^2=1 ?

The answer to whether tan^2(x+c)+1-(tan(x+c))^2=1 is True

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prove tan^2(x+c)+1-(tan(x+c))^2=1

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (x + c) + 1 - (tan (x + c))^{2}

Simplify

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

Simplify

= 1

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (x) = sin (x)

cos (x) (cot (x) + tan (x)) = csc (x)

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

\frac{2 cos ( x )}{cos ^{2} ( x )} = 2 sec (x)

cos (x + π) + sin (x - \frac{3 π}{2}) = 0

Is tan^2(x+c)+1-(tan(x+c))^2=1 ?
The answer to whether tan^2(x+c)+1-(tan(x+c))^2=1 is True