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

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

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

prove

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

True

Solution steps

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

Manipulating right side

tan (a) + 1

Express with sin, cos

1 + tan (a)

Use the basic trigonometric identity:

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

= 1 + \frac{sin ( a )}{cos ( a )}

Simplify

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

1 + \frac{sin ( a )}{cos ( a )}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

Multiply:

1 \cdot cos (a) = cos (a)

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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