Is sec(x)+1=(cos(x)+1)/(cos(x)) ?

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

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prove sec(x)+1=(cos(x)+1)/(cos(x))

prove

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

True

Solution steps

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

Manipulating left side

sec (x) + 1

Express with sin, cos

1 + sec (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

Multiply:

1 \cdot cos (x) = cos (x)

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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3 sin (x^{2}) + 4 cos^{2} (x) = 3 + cos^{2} (x)

\frac{1 - csc ( x )}{sec ( x )} = cot (x) cos (x)

cos (9 0^{\circ} + 3 0^{\circ}) = cos (12 0^{\circ})

sin (θ) cos (θ) = sin (θ)

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