Is sin(a)cot(a)=cos(a) ?

The answer to whether sin(a)cot(a)=cos(a) is True

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prove sin(a)cot(a)=cos(a)

prove

sin (a) cot (a) = cos (a)

True

Solution steps

sin (a) cot (a) = cos (a)

Manipulating left side

sin (a) cot (a)

Express with sin, cos

cot (a) sin (a)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (a)

= cos (a)

= cos (a)

= cos (a)

We showed that the two sides could take the same form

\Rightarrow True

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

cos^{2} (B) - sin^{2} (B) = 2 cos^{2} (B) - 1

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