Is tan(x)cot(x)=sin^2(x)+cos^2(x) ?

The answer to whether tan(x)cot(x)=sin^2(x)+cos^2(x) is True

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prove tan(x)cot(x)=sin^2(x)+cos^2(x)

prove

tan (x) cot (x) = sin^{2} (x) + cos^{2} (x)

True

Solution steps

tan (x) cot (x) = sin^{2} (x) + cos^{2} (x)

Manipulating left side

tan (x) cot (x)

Express with sin, cos

cot (x) tan (x)

Use the basic trigonometric identity:

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

= \frac{cos ( x )}{sin ( x )} tan (x)

Use the basic trigonometric identity:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{cos ( x )}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )}

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

\frac{cos ( x )}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

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

Cancel the common factor:

sin (x)

= 1

= 1

= 1

Rewrite using trig identities

1

Use the Pythagorean identity:

1 = cos^{2} (x) + sin^{2} (x)

= cos^{2} (x) + sin^{2} (x)

= cos^{2} (x) + sin^{2} (x)

= sin^{2} (x) + cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

7 \frac{cot ^{2} ( x )}{csc ( x )} sec^{2} (x) = 7 tan (x) cos (x) csc^{2} (x)

cos^{2} (x) = 1 + sin^{2} (x)

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

cos (θ) = - \frac{7}{10}

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