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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sin (A) cos (A) tan (A)

Express with sin, cos

cos (A) sin (A) tan (A)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (A)

= sin (A) sin (A)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

sin (A) sin (A) = sin^{1 + 1} (A)

= sin^{1 + 1} (A)

Add the numbers:

1 + 1 = 2

= sin^{2} (A)

= sin^{2} (A)

= sin^{2} (A)

We showed that the two sides could take the same form

\Rightarrow True

sin (\frac{4 π}{3}) = 3 cos (\frac{2 π}{3})

\frac{sin ( 2 x ) + sin ( 6 x )}{cos ( 2 x ) - cos ( 6 x )} = cot (2 x)

sin^{2} (x) + sin^{2} (θ) = 1

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

tan^{2} (0) = - tan (0)

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