Question

prove that 1-cosA/sinA=tanA/2

Answer 1

this is the answer i thought

Answer 2

Answer: Proved.

Step-by-step explanation:  We are given to prove the following equality -

$\dfrac{1-\cos A}{\sin A}=\tan\dfrac{A}{2}.$

To prove the above, we need to recall the following popular identities from Trigonometry -

$1-\cos \theta=2\sin^2\dfrac{\theta}{2}\\\\\textup{and}\\\\\sin \theta=2\sin\dfrac{\theta}{2}\cos\dfrac{\theta}{2}.$

Applying these two identities, we try to prove the given result as follows.

$L.H.S\\\\=\dfrac{1-\cos A}{\sin A}\\\\=\dfrac{2\sin^2\dfrac{A}{2}}{2\sin\dfrac{A}{2}\cos\dfrac{A}{2}}\\\\\\=\dfrac{\sin\dfrac{A}{2}}{\cos\dfrac{A}{2}}\\\\\\=\tan\dfrac{A}{2}\\\\=R.H.S.$

Hence proved.