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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

prove

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

True

Solution steps

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

Manipulating right side

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

Expand

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

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

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

Apply the distributive law:

a (b + c) = ab + a c

a = tan (x), b = 1, c = cos (x)

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

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

Multiply:

1 \cdot tan (x) = tan (x)

= tan (x) + tan (x) cos (x)

= tan (x) + cos (x) tan (x)

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

= sin (x)

= tan (x) + sin (x)

= tan (x) + sin (x)

= sin (x) + tan (x)

We showed that the two sides could take the same form

\Rightarrow True

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

sin (\frac{3 π}{2} - 0) = - cos (0)

sin (x) + cos (2 x) = 4 sin^{2} (x) - 1

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

tan (- θ) = tan (θ)

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