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

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

csc (x) sin (x) = 1

csc (x) sin (x)

Express with sin, cos

csc (x) sin (x)

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( x )} sin (x)

\frac{1}{sin ( x )} sin (x) = 1

\frac{1}{sin ( x )} sin (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 sin ( x )}{sin ( x )}

Cancel the common factor:

sin (x)

= 1

= 1

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

Apply rule

\frac{a}{1} = a

\frac{1}{1} = 1

= tan^{2} (x) + 1

Use the Pythagorean identity:

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

= sec^{2} (x)

= 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

1 + cos (2 t) = cot (t) sin (2 t)

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