Is tan(θ)+1=(cos(θ)+sin(θ))/(cos(θ)) ?

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

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prove tan(θ)+1=(cos(θ)+sin(θ))/(cos(θ))

prove

tan (θ) + 1 = \frac{cos ( θ ) + sin ( θ )}{cos ( θ )}

True

Solution steps

tan (θ) + 1 = \frac{cos ( θ ) + sin ( θ )}{cos ( θ )}

Manipulating left side

tan (θ) + 1

Express with sin, cos

1 + tan (θ)

Use the basic trigonometric identity:

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

= 1 + \frac{sin ( θ )}{cos ( θ )}

Simplify

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

1 + \frac{sin ( θ )}{cos ( θ )}

Convert element to fraction:

1 = \frac{1 cos ( θ )}{cos ( θ )}

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

Multiply:

1 \cdot cos (θ) = cos (θ)

= \frac{cos ( θ ) + sin ( θ )}{cos ( θ )}

= \frac{cos ( θ ) + sin ( θ )}{cos ( θ )}

= \frac{cos ( θ ) + sin ( θ )}{cos ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

- \frac{1}{2} = 2 sin (- \frac{π}{12}) cos (- \frac{π}{12})

sec^{4} (x) = tan^{4} (x)

1 - cos (\frac{π}{n}) = 2 sin^{2} (\frac{π}{2 n})

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

cos (\frac{7 π}{12}) = cos (\frac{π}{3} + \frac{π}{4})

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