Is (sec(x))/(cos(x))= 1/(cos^2(x)) ?

The answer to whether (sec(x))/(cos(x))= 1/(cos^2(x)) is True

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prove (sec(x))/(cos(x))= 1/(cos^2(x))

prove

\frac{sec ( x )}{cos ( x )} = \frac{1}{cos ^{2} ( x )}

True

Solution steps

\frac{sec ( x )}{cos ( x )} = \frac{1}{cos ^{2} ( x )}

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

= \frac{\frac{1}{c o s ( x )}}{cos ( x )}

Simplify

\frac{\frac{1}{c o s ( x )}}{cos ( x )} : \frac{1}{cos ^{2} ( x )}

\frac{\frac{1}{c o s ( x )}}{cos ( x )}

Apply the fraction rule:

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

= \frac{1}{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{1}{cos ^{2} ( x )}

= \frac{1}{cos ^{2} ( x )}

= \frac{1}{cos ^{2} ( x )}

We showed that the two sides could take the same form

\Rightarrow True

tan (θ) = csc (θ) sec (θ) - cot (θ)

sec (x) - sec (x) sin (x^{2}) = cos (x^{2})

tan^{2} (3 π) = tan (3 π)

(1 + cot^{2} (x)) = \frac{1}{sin ^{2} ( x )}

sin (x) (1 + csc (x)) = 1 + sin (x)

Is (sec(x))/(cos(x))= 1/(cos^2(x)) ?
The answer to whether (sec(x))/(cos(x))= 1/(cos^2(x)) is True