Is cos(x)tan(x)+sin(x)=2sin(x) ?

The answer to whether cos(x)tan(x)+sin(x)=2sin(x) is True

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prove cos(x)tan(x)+sin(x)=2sin(x)

prove

cos (x) tan (x) + sin (x) = 2 sin (x)

True

Solution steps

cos (x) tan (x) + sin (x) = 2 sin (x)

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

sin (x) + cos (x) \frac{sin ( x )}{cos ( x )} : 2 sin (x)

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

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)

= sin (x) + sin (x)

Add similar elements:

sin (x) + sin (x) = 2 sin (x)

= 2 sin (x)

= 2 sin (x)

= 2 sin (x)

We showed that the two sides could take the same form

\Rightarrow True

2 sin (x) cos (x) - tan (x) = tan (x) cos (2 x)

\frac{csc ( θ )}{csc ( θ ) - sin ( θ )} = sec^{2} (θ)

cos (x) sec (x) = tan (x) cot (x)

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

\frac{csc ( x )}{1 + cot ^{2} ( x )} = sin (x)

Is cos(x)tan(x)+sin(x)=2sin(x) ?
The answer to whether cos(x)tan(x)+sin(x)=2sin(x) is True