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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= 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)

= cos^{2} (x)

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

(3 sin (θ) + 3 cos (θ))^{2} = 9 + 9 sin (2 θ)

tan (x) - \frac{sec ^{2} ( x )}{tan ( x )} = - cot (x)

\frac{tan ^{2} ( θ ) + 1}{tan ^{2} ( θ )} = csc^{2} (θ)

sec^{2} (x) csc^{2} (x) - sec^{2} (x) = csc^{2} (x)

\frac{sec ( A ) - cos ( A )}{csc ( A ) - sin ( A )} = tan^{3} (A)

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