Is csc(x)-cos(x)tan(x)=csc(x)-sin(x) ?

The answer to whether csc(x)-cos(x)tan(x)=csc(x)-sin(x) is True

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prove csc(x)-cos(x)tan(x)=csc(x)-sin(x)

prove

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

True

Solution steps

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

Manipulating left side

csc (x) - cos (x) tan (x)

Rewrite using trig identities

csc (x) - cos (x) tan (x)

Use the basic trigonometric identity:

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

= csc (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)

= csc (x) - sin (x)

= csc (x) - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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

sin^{6} (a) + cos^{6} (a) = 1 - 3 sin^{2} (a) \cdot cos^{2} (a)

sin (- 3 x) = - sin (3 x)

2 tan (θ) = sin (θ)

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

Is csc(x)-cos(x)tan(x)=csc(x)-sin(x) ?
The answer to whether csc(x)-cos(x)tan(x)=csc(x)-sin(x) is True