Is 2cos(θ)= 2/(sec(θ)) ?

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

Popular >

prove 2cos(θ)= 2/(sec(θ))

prove

2 cos (θ) = \frac{2}{sec ( θ )}

True

Solution steps

2 cos (θ) = \frac{2}{sec ( θ )}

Manipulating right side

\frac{2}{sec ( θ )}

Express with sin, cos

\frac{2}{sec ( θ )}

Use the basic trigonometric identity:

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

= \frac{2}{\frac{1}{c o s ( θ )}}

Simplify

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

\frac{2}{\frac{1}{c o s ( θ )}}

Apply the fraction rule:

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

= \frac{2 cos ( θ )}{1}

Apply rule

\frac{a}{1} = a

= 2 cos (θ)

= 2 cos (θ)

= 2 cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

(1 + sin (θ)) (1 - sin (θ)) = cos^{2} (x)

sin^{2} (θ) = csc (θ)

\frac{1 - cot ( a )}{csc ( a )} = sin (a) - cos (a)

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

2 sin (x^{2}) - sin (x) - 3 = 0