Is cot(x)+5=5+csc(x)*cos(x) ?

The answer to whether cot(x)+5=5+csc(x)*cos(x) is True

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prove cot(x)+5=5+csc(x)*cos(x)

prove

cot (x) + 5 = 5 + csc (x) \cdot cos (x)

True

Solution steps

cot (x) + 5 = 5 + csc (x) cos (x)

Manipulating right side

5 + csc (x) cos (x)

Rewrite using trig identities

5 + csc (x) cos (x)

Express with sin, cos

csc (x) cos (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Multiply:

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

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

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

= 5 + \frac{cos ( x )}{sin ( x )}

Use the basic trigonometric identity:

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

= 5 + cot (x)

= 5 + cot (x)

= cot (x) + 5

We showed that the two sides could take the same form

\Rightarrow True

csc (θ) = cos (θ) cot (θ) + sin^{2} (θ) csc (θ)

cos (y) csc (y) = cot (y)

\frac{tan ( a )}{sin ( a )} - sec (a) = 0

\frac{1}{cot ( θ )} = \frac{tan ( θ )}{sin ( θ )}

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

Is cot(x)+5=5+csc(x)*cos(x) ?
The answer to whether cot(x)+5=5+csc(x)*cos(x) is True