Question

sinA/(1+cosA) = cosecA - cotA​

Answer 1

Answer:

Step-by-step explanation:

sinA/(1+cosA)

= SinA(1-cosA)/(1+cosA)(1-cosA)

= sinA (1-cosA)/1-cos^2A)

= SinA(1-cosA)/sin^A

= (1-cosA)/sinA

= 1/sinA - cosA/sinA

= cosecA - cotA

Hence proved LHS = RHS

Answer 2

Answer:

cosecA - cotA​

Step-by-step explanation:

sinA/(1+cosA)

we should rationalise the denominator

sinA/(1+cosA)×(1-cosA)/(1-cosA)

sinA[1-cosA]/[1+cosA][1-cosA]

sinA[1-cos A]/[1-cos²A]

sinA [1-cos A]/sin²A

1-cosA/sinA

∴cosecA - cotA​