Is sec(θ)+1=(cos(θ)+1)/(cos(θ)) ?

The answer to whether sec(θ)+1=(cos(θ)+1)/(cos(θ)) is True

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prove sec(θ)+1=(cos(θ)+1)/(cos(θ))

prove

sec (θ) + 1 = \frac{cos ( θ ) + 1}{cos ( θ )}

True

Solution steps

sec (θ) + 1 = \frac{cos ( θ ) + 1}{cos ( θ )}

Manipulating left side

sec (θ) + 1

Express with sin, cos

1 + sec (θ)

Use the basic trigonometric identity:

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

= 1 + \frac{1}{cos ( θ )}

Simplify

1 + \frac{1}{cos ( θ )} : \frac{cos ( θ ) + 1}{cos ( θ )}

1 + \frac{1}{cos ( θ )}

Convert element to fraction:

1 = \frac{1 cos ( θ )}{cos ( θ )}

= \frac{1 \cdot cos ( θ )}{cos ( θ )} + \frac{1}{cos ( θ )}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot cos ( θ ) + 1}{cos ( θ )}

Multiply:

1 \cdot cos (θ) = cos (θ)

= \frac{cos ( θ ) + 1}{cos ( θ )}

= \frac{cos ( θ ) + 1}{cos ( θ )}

= \frac{1 + cos ( θ )}{cos ( θ )}

= \frac{cos ( θ ) + 1}{cos ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

9 sin (7 π - x) = 9 sin (x)

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

1 + sin (4 a) + sin (2 a) = cos (2 a)

\frac{1}{cos ( θ ) sin ( θ )} = \frac{csc ( θ )}{cos ( θ )}

sin (2 x) = sin (x) + 1

Is sec(θ)+1=(cos(θ)+1)/(cos(θ)) ?
The answer to whether sec(θ)+1=(cos(θ)+1)/(cos(θ)) is True