Is 1/(tan(b))+tan(b)=(sec^2(b))/(tan(b)) ?

The answer to whether 1/(tan(b))+tan(b)=(sec^2(b))/(tan(b)) is True

Popular >

prove 1/(tan(b))+tan(b)=(sec^2(b))/(tan(b))

prove

\frac{1}{tan ( b )} + tan (b) = \frac{sec ^{2} ( b )}{tan ( b )}

True

Solution steps

\frac{1}{tan ( b )} + tan (b) = \frac{sec ^{2} ( b )}{tan ( b )}

Manipulating left side

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

Simplify

\frac{1}{tan ( b )} + tan (b) : \frac{1 + tan ^{2} ( b )}{tan ( b )}

= \frac{1 + tan ^{2} ( b )}{tan ( b )}

Rewrite using trig identities

= \frac{sec ^{2} ( b )}{tan ( b )}

We showed that the two sides could take the same form

\Rightarrow True

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

sin (2 a) = 2 sin (a)

cos^{3} (x) = (cos (x))^{3}

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

cos (b) (1 + tan (b))^{2} = sec (b) + 2 sin (b)

Is 1/(tan(b))+tan(b)=(sec^2(b))/(tan(b)) ?
The answer to whether 1/(tan(b))+tan(b)=(sec^2(b))/(tan(b)) is True