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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos^{2} (x)

= sin^{2} (x)

= sin^{2} (x)

= sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e \frac{1}{1 + tan ^{2} ( x )} - \frac{1}{1 + cot ^{2} ( x )} = 1

p ro v e csc^{2} (x) - 1 = (csc (x) - 1) (csc (x) + 1)

p ro v e csc^{4} (x) (cot^{2} (x)) = csc^{3} (x)

p ro v e cos (x^{2}) = \frac{1}{sec ( x ^{2} )}

p ro v e cot (x) + tan (x) = \frac{2}{sin ( 2 x )}

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