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

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

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prove cot^2(x)+1/(cos(x)sec(x))=csc^2(x)

prove

cot^{2} (x) + \frac{1}{cos ( x ) sec ( x )} = csc^{2} (x)

True

Solution steps

cot^{2} (x) + \frac{1}{cos ( x ) sec ( x )} = csc^{2} (x)

Manipulating left side

cot^{2} (x) + \frac{1}{cos ( x ) sec ( x )}

Rewrite using trig identities

= csc^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

tan^{2} (θ) = sec^{2} (θ) - 1

(1 + sec (θ)) (1 - sec (θ)) = - tan^{2} (θ)

cos (x) = \frac{cot ( x )}{csc ( x )}

sin (\frac{3 π}{2} - x) = - cos (x)

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