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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 tan^{2} (x)

Express with sin, cos

2 tan^{2} (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

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

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

= 2 \cdot \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

Multiply fractions:

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

= \frac{sin ^{2} ( x ) \cdot 2}{cos ^{2} ( x )}

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

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

We showed that the two sides could take the same form

\Rightarrow True

csc (θ) \cdot tan (θ) = sec (θ)

cot (θ) \cdot csc (θ) \cdot sec (θ) = csc^{2} (θ)

sin (x) + cos (x) + cot (x) = csc (x)

sin^{2} (α) + sin^{2} (α) tan^{2} (α) = tan^{2} (α)

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

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