Is (sec(x)-1)/(sin(x)sec(x))=tan(x/2) ?

The answer to whether (sec(x)-1)/(sin(x)sec(x))=tan(x/2) is True

Popular >

prove (sec(x)-1)/(sin(x)sec(x))=tan(x/2)

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

\frac{sec ( 2 u ) - 1}{sin ( 2 u ) sec ( 2 u )} = tan (u)

Prove

\frac{sec ( 2 u ) - 1}{sin ( 2 u ) sec ( 2 u )} = tan (u) :

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

cos (4 x) - sin (4 x) = cos (2 x)

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

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

cos^{2} (3 x) - sin^{2} (3 x) = cos (6 x)

sec^{2} (Θ) csc^{2} (Θ) = sec^{2} (Θ) + csc^{2} (Θ)

Is (sec(x)-1)/(sin(x)sec(x))=tan(x/2) ?
The answer to whether (sec(x)-1)/(sin(x)sec(x))=tan(x/2) is True