Evaluate the expression. $\tan \frac { a } { 2 }$
A) $\cos a + \cot a$
B) $\cos a - \cot a$
C) $\csc a - \cot a$
D) $\csc a - \tan a$
E) $\csc a + \cot a$

Question

Evaluate the expression. $\tan \frac { a } { 2 }$ 
A) $\cos a + \cot a$
B) $\cos a - \cot a$
C) $\csc a - \cot a$
D) $\csc a - \tan a$
E) $\csc a + \cot a$

Quizplus · Accepted Answer

The correct expression for $\tan \frac { a } { 2 }$ can be derived using the half-angle identity for tangent, which is $\tan \frac { a } { 2 } = \frac {1 - \cos a}{\sin a}$. This can be rewritten as $\frac {\sin a}{\cos a + 1}$, which simplifies to $\csc a - \cot a$ when you apply the reciprocal and quotient identities of trigonometric functions.

Evaluate the Expression tan⁡a2\tan \frac { a } { 2 }tan2a​

Evaluate the Expression $\tan \frac { a } { 2 }$