How do you verify $tan (\frac{A}{2}) = csc A - cot A$ $tan(A/2)=cscA-cotA$ ?

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Answer 1 · 2016-04-16T22:56:08

See below

LHS=left hand side, RHS =right hand side

Use formula $tan (\frac{1}{2} A) = \frac{1 - cos x}{sin x}$ $tan (1/2 A) =(1-cosx)/sinx$

LHS $= \frac{1 - cos x}{sin x}$ $=(1-cosx)/sinx$

$= \frac{1}{sin x} - \frac{cos x}{sin x}$ $=1/sinx - cosx/sinx$

$= csc x - cot x$ $=csc x - cot x$

$= R H S$ $=RHS$

How do you verify tan(A2)=cscA−cotAtan(A/2)=cscA-cotA?