Is 1/(tan(x))+tan(x)=sec(x)csc(x) ?

The answer to whether 1/(tan(x))+tan(x)=sec(x)csc(x) is True

Popular >

prove 1/(tan(x))+tan(x)=sec(x)csc(x)

prove

\frac{1}{tan ( x )} + tan (x) = sec (x) csc (x)

True

Solution steps

\frac{1}{tan ( x )} + tan (x) = sec (x) csc (x)

Manipulating left side

\frac{1}{tan ( x )} + tan (x)

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

sec (x) csc (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (\frac{π}{2} - x) = sin (\frac{π}{2} + x)

\frac{sin ^{2} ( t )}{cos ( t )} = sec (t) - cos (t)

tan (θ) + cot (θ) = 2 csc (2 θ)

csc^{4} (x) - cot^{4} (x) = 2 cot^{2} (x) + 1

(1 - sin^{2} (x)) tan^{2} (x) = sin^{2} (x)

Is 1/(tan(x))+tan(x)=sec(x)csc(x) ?
The answer to whether 1/(tan(x))+tan(x)=sec(x)csc(x) is True