Is tan^2(x)+1/(sin(x)csc(x))=sec^2(x) ?

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

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prove tan^2(x)+1/(sin(x)csc(x))=sec^2(x)

prove

tan^{2} (x) + \frac{1}{sin ( x ) csc ( x )} = sec^{2} (x)

True

Solution steps

tan^{2} (x) + \frac{1}{sin ( x ) csc ( x )} = sec^{2} (x)

Manipulating left side

tan^{2} (x) + \frac{1}{sin ( x ) csc ( x )}

Rewrite using trig identities

= sec^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

csc (- x) - sin (- x) = cos (- x) cot (- x)

(csc (x)) (tan (x)) = sec (x)

cot (\frac{x}{2}) = \frac{1 + cos ( x )}{sin ( x )}

(sin (x)) (csc (x)) = 1

sin (α) = \frac{2 tan ( \frac{α}{2} )}{1 + tan ^{2} ( \frac{α}{2} )}

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