Is sin(a)cos(a)=cos^2(a)tan(a) ?

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

Popular >

prove sin(a)cos(a)=cos^2(a)tan(a)

prove

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

True

Solution steps

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

Manipulating right side

cos^{2} (a) tan (a)

Express with sin, cos

cos^{2} (a) tan (a)

Use the basic trigonometric identity:

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

= cos^{2} (a) \frac{sin ( a )}{cos ( a )}

Simplify

cos^{2} (a) \frac{sin ( a )}{cos ( a )} : sin (a) cos (a)

cos^{2} (a) \frac{sin ( a )}{cos ( a )}

Multiply fractions:

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

= \frac{sin ( a ) cos ^{2} ( a )}{cos ( a )}

Cancel the common factor:

cos (a)

= sin (a) cos (a)

= sin (a) cos (a)

= cos (a) sin (a)

= sin (a) cos (a)

We showed that the two sides could take the same form

\Rightarrow True

(cos (x)) (tan (x)) (csc (x)) = 1

\frac{csc ( x ) tan ( x )}{1 + tan ( x )} = cos (x)

sin (- \frac{π}{4}) = - sin (\frac{π}{4})

1 - 2 sin^{4} (x) = 1 - 2 sin^{2} (x)

sin (z + w) = sin (z) cos (w) + cos (z) sin (w)

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