Is cos(x)sin(x)=(sin(x))/(sec(x)) ?

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

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prove cos(x)sin(x)=(sin(x))/(sec(x))

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= sin (x) cos (x)

= sin (x) cos (x)

= cos (x) sin (x)

We showed that the two sides could take the same form

\Rightarrow True

- sin^{2} (θ) = cos^{2} (θ)

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

sec^{2} (x) cot^{2} (x) = cot^{2} (x) + 1

1 + tan^{2} (B) = sec^{2} (B)

sec (\frac{3 π}{4}) = - 2

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