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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

= sin (x) sin (x)

Apply exponent rule:

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

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

= sin^{1 + 1} (x)

Add the numbers:

1 + 1 = 2

= sin^{2} (x)

= sin^{2} (x)

= sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{cot ^{2} ( t )}{csc ( t )} = csc (t) - sin (t)

cos (π - θ) = - cos (θ)

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

cot (x) + tan (x) = csc (x) sec (x)

\frac{sec ( θ ) - 1}{1 - cos ( θ )} = sec (θ)

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