Question

sin tita /1-cos tita = cosec tita + cot tita

Answer 1

Given :-

• Sin∅ / 1 - cos∅

To Find :-

• Cosec∅ + cot∅

Now,

→ Sin∅ / 1 - cos∅

• Rationalising it

→ (Sin∅ / 1 - cos∅) ( 1 + cos∅ / 1 + cos∅ )

→ sin∅ ( 1 + cos∅ ) / 1 - cos²∅

→ sin∅ + sin∅cos∅ / sin²∅

→ sin∅ ( 1 + cos∅ ) /sin²∅

→ (1 + cos∅) / sin∅

→ 1/sin∅ + cos∅ / sin∅

→ cosec∅ + cot∅

Hence, Proved.

Answer 2

= Sinθ/(1 – cosθ) + Tanθ/(1 + cosθ)

= (sinθ(1 + cosθ) + Tanθ(1-Cosθ))/(1 – Cos²θ)

= (sinθ(1 + cosθ) + (Tanθ – Sinθ)) /Sin²θ

= ( 1 + cosθ + 1/Cosθ – 1)/Sinθ

$\sf= (cosθ + 1/Cosθ)/Sinθ$

$\sf \: = \frac{1}{CosθSinθ }+ \frac{cosθ}{ Sinθ}$

$\sf=\: Cosecθ + Cotθ$

Hence Proved.

RHS.

See Attachment.