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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (x) + sin (x) csc (x)

Rewrite using trig identities

tan^{2} (x) + 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) + 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

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

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

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

(1 - cos (x)) (1 + sec (x)) = 1

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

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