Question

Pls help... Boards are near
I will mark best answer as brainliest

Answer 1

Answer in attachment. Hope it helps.

Answer 2

In this question, we have to prove LHS = RHS.

1/ (cosec∅ + cot∅) - 1/sin∅ =   1/sin∅ - 1/ (cosec∅ -cot∅)

Taking LHS,

= 1/ (cosec∅ + cot∅) - 1/sin∅

cosec∅ = 1/sin∅        cot∅ = cos∅/sin∅

= 1/(1/sin∅ + cos∅/sin∅) - 1/ sin∅

= sin∅/(1+cos∅) - 1/ sin∅

= sin²∅-1-cos∅ / sin∅(1+cos∅)

= 1-cos²∅-1-cos∅ / sin∅(1+cos∅)

= -cos∅(1+cos∅) / sin∅ (1+cos∅)

LHS = -cos∅/ sin∅

Now, taking RHS,

= 1/sin∅ - 1/ (cosec∅ - cot∅)

= 1/sin∅ - 1/ (1/sin∅ - cos∅/sin∅)

= 1/sin∅ - sin∅/(1-cos∅)

= 1-cos∅-sin²∅ / (sin∅(1-cos∅)

= 1-cos∅-(1-cos²∅) / (sin∅(1-cos∅)

= 1-cos∅-1+cos²∅ / (sin∅(1-cos∅)

= -cos∅ (1-cos∅) / sin∅ (1-cos∅)

RHS = -cos∅/ sin∅

LHS = RHS

Hence proved.