Is cos(x)(tan(x)+1)=sin(x)+cos(x) ?

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

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prove cos(x)(tan(x)+1)=sin(x)+cos(x)

prove

cos (x) (tan (x) + 1) = sin (x) + cos (x)

True

Solution steps

cos (x) (tan (x) + 1) = sin (x) + cos (x)

Manipulating left side

cos (x) (tan (x) + 1)

Express with sin, cos

(1 + tan (x)) cos (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Join

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

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

Convert element to fraction:

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

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

Multiply:

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

= cos (x) + sin (x)

= cos (x) + sin (x)

= cos (x) + sin (x)

= sin (x) + cos (x)

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (x) + sec^{2} (x) = 1 + 2 tan^{2} (x)

\frac{sin ( 2 a )}{1 + cos ( 2 a )} = tan (a)

tan (x) = tan (x + π)

1 + csc (a) = csc (a) (1 + sin (a))

1 + cot (θ) = csc (θ) (cos (θ) + sin (θ))

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