Is sin(x)= 3/4*(sin(x))/(3/4) ?

The answer to whether sin(x)= 3/4*(sin(x))/(3/4) is True

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prove sin(x)= 3/4*(sin(x))/(3/4)

prove

sin (x) = \frac{3}{4} \cdot \frac{sin ( x )}{\frac{3}{4}}

True

Solution steps

sin (x) = \frac{3}{4} \cdot \frac{sin ( x )}{\frac{3}{4}}

Manipulating right side

\frac{3}{4} \frac{sin ( x )}{\frac{3}{4}}

Simplify

\frac{3}{4} \frac{sin ( x )}{\frac{3}{4}} : sin (x)

\frac{3}{4} \cdot \frac{sin ( x )}{\frac{3}{4}}

Apply the fraction rule:

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

= \frac{3}{4} \cdot \frac{4 sin ( x )}{3}

Multiply fractions:

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

= \frac{3 sin ( x ) \cdot 4}{4 \cdot 3}

Cancel the common factor:

3

= \frac{sin ( x ) \cdot 4}{4}

Cancel the common factor:

4

= sin (x)

= sin (x)

We showed that the two sides could take the same form

\Rightarrow True

(tan (x) + 2) = 2 + sec (x) sin (x)

tan (θ - 4 5^{\circ}) + tan (θ + 4 5^{\circ}) = 2 tan (2 θ)

tan (2 θ) - tan (θ) = tan (θ) sec (2 θ)

\frac{sin ( x )}{csc ( x )} = sin^{2} (x)

tan (2 A) - tan (A) = tan (A) sec (2 A)

Is sin(x)= 3/4*(sin(x))/(3/4) ?
The answer to whether sin(x)= 3/4*(sin(x))/(3/4) is True