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

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

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prove tan(a)*cot(a)=sin^2(a)+cos^2(a)

prove

tan (a) \cdot cot (a) = sin^{2} (a) + cos^{2} (a)

True

Solution steps

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

Manipulating left side

tan (a) cot (a)

Express with sin, cos

cot (a) tan (a)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (a)

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

Cancel the common factor:

sin (a)

= 1

= 1

= 1

Rewrite using trig identities

1

Use the Pythagorean identity:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

sin (x) cos (x) = tan (x)

cot (\frac{15 π}{8}) = cot (\frac{7 π}{8})

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

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

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