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

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

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

prove

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

True

Solution steps

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

We showed that the two sides could take the same form

\Rightarrow True

tan (a) + cot (a) = \frac{2}{sin ( 2 a )}

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

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

\frac{1 + sin ( α )}{cos ( α )} = \frac{cos ( α )}{1 - sin ( α )}

2 csc^{2} (y) = \frac{1}{1 - cos ( y )} + \frac{1}{1 + cos ( y )}

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