Is csc(x)tan(x)cos^2(x)=cos(x) ?

The answer to whether csc(x)tan(x)cos^2(x)=cos(x) is True

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prove csc(x)tan(x)cos^2(x)=cos(x)

prove

csc (x) tan (x) cos^{2} (x) = cos (x)

True

Solution steps

csc (x) tan (x) cos^{2} (x) = cos (x)

Manipulating left side

csc (x) tan (x) cos^{2} (x)

Express with sin, cos

cos^{2} (x) csc (x) tan (x)

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= cos^{2} (x) \frac{1}{sin ( x )} tan (x)

Use the basic trigonometric identity:

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

= cos^{2} (x) \frac{1}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Simplify

cos^{2} (x) \frac{1}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )} : cos (x)

cos^{2} (x) \frac{1}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Multiply fractions:

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

= \frac{1 \cdot sin ( x ) cos ^{2} ( x )}{sin ( x ) cos ( x )}

Cancel the common factor:

sin (x)

= \frac{1 \cdot cos ^{2} ( x )}{cos ( x )}

Multiply:

1 \cdot cos^{2} (x) = cos^{2} (x)

= \frac{cos ^{2} ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= cos (x)

= cos (x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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

sin (a) sin (b) = sin (a + b)

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

2 sin (x) = \frac{( 4 cos ( x ) - 1 )}{tan ( x )}

\frac{( 1 - cos ( 4 x ) + sin ( 4 x ) )}{( 1 + cos ( 4 x ) + sin ( 4 x ) )} = 3 sin (2 x)

Is csc(x)tan(x)cos^2(x)=cos(x) ?
The answer to whether csc(x)tan(x)cos^2(x)=cos(x) is True