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

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

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

prove

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

True

Solution steps

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

Manipulating right side

tan (x) sec (x)

Express with sin, cos

sec (x) tan (x)

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( x )} tan (x)

Use the basic trigonometric identity:

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

= \frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Simplify

\frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )} : \frac{sin ( x )}{cos ^{2} ( x )}

\frac{1}{cos ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Multiply fractions:

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

= \frac{1 \cdot sin ( x )}{cos ( x ) cos ( x )}

Multiply:

1 \cdot sin (x) = sin (x)

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

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

cos (x) cos (x)

Apply exponent rule:

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

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

= cos^{1 + 1} (x)

Add the numbers:

1 + 1 = 2

= cos^{2} (x)

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

(sec (x)) (sin (x)) = tan (x)

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

sin^{3} (z) cos^{2} (z) = sin^{3} (z) - sin^{5} (z)

\frac{cos ( x ) sec ( x )}{cot ( x ) tan ( x )} = 1

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