Question

sin A / 1+cos A =cosec A - cot A​

Answer 1

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Answer 2

Step-by-step explanation:

LHS = sin A / 1+cos A

By multiplying with 1 - Cos A both the sides,

We get,

⇒ [sin A/ 1+cosA ] [1-cosA / 1-cosA]

⇒ [(sin A)(1-cosA)] / [(1+cosA)(1-cosA)]

The denominator is in the form,

⇒ (a + b)(a - b),.

Hence,

We can use this identity : (a - b)(a + b) = a² - b²

⇒ [sinA - sinAcosA] / [1 - cos^2A]

⇒ sinA [1-cosA] / sin^2A

We know that,

⇒ Sin² A + Cos² A = 1

∴ Sin²A = 1 - Cos² A

⇒ [1 - cosA] / sinA

Hence Proved

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