Is csc^2(u)-cos(u)sec(u)=cot^2(u) ?

The answer to whether csc^2(u)-cos(u)sec(u)=cot^2(u) is True

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prove csc^2(u)-cos(u)sec(u)=cot^2(u)

prove

csc^{2} (u) - cos (u) sec (u) = cot^{2} (u)

True

Solution steps

csc^{2} (u) - cos (u) sec (u) = cot^{2} (u)

Manipulating left side

csc^{2} (u) - cos (u) sec (u)

Rewrite using trig identities

csc^{2} (u) - cos (u) sec (u)

sec (u) cos (u) = 1

sec (u) cos (u)

Express with sin, cos

sec (u) cos (u)

Use the basic trigonometric identity:

sec (u) = \frac{1}{cos ( u )}

= \frac{1}{cos ( u )} cos (u)

\frac{1}{cos ( u )} cos (u) = 1

\frac{1}{cos ( u )} cos (u)

Multiply fractions:

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

= \frac{1 cos ( u )}{cos ( u )}

Cancel the common factor:

cos (u)

= 1

= 1

= csc^{2} (u) - 1

Use the Pythagorean identity:

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

csc^{2} (x) - 1 = cot^{2} (x)

= cot^{2} (u)

= cot^{2} (u)

We showed that the two sides could take the same form

\Rightarrow True

Is csc^2(u)-cos(u)sec(u)=cot^2(u) ?
The answer to whether csc^2(u)-cos(u)sec(u)=cot^2(u) is True