Question

sin /1 + cos A + 1 + cos A/ sin A = cosec A​

Answer 1

Answer:

Sin 1783=cosec A

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Answer 2

Step-by-step explanation:

I believe your Question was,

"Prove that :-

(SinA/(1 + CosA)) + ((1 + CosA)/SinA) = 2CosecA"

Now,

(SinA/(1 + CosA)) + ((1 + CosA)/SinA)

Solving,

(SinA × SinA) + ((1 + CosA)(1 + CosA)/(SinA)(1 + CosA)

((Sin²A) + (1 + CosA)²)/(SinA)(1 + CosA)

((Sin²A) + (1² + 2(1)(CosA) + Cos²A))/(SinA)(1 + CosA)

(Sin²A + Cos²A + 1 + 2CosA)/(SinA)(1 + CosA)

((Sin²A + Cos²A) + 1 + 2CosA)/(SinA)(1 + CosA)

We know that,

(Sin²A + Cos²A) = 1

((1) + 1 + 2CosA)/(SinA)(1 + CosA)

(1 + 1 + 2CosA)/(SinA)(1 + CosA)

(2 + 2CosA)/(SinA)(1 + CosA)

2(1 + CosA)/(SinA)(1 + CosA)

Cancelling the common terms,

2/SinA

We know that,

1/SinA = CosecA

Thus,

2/SinA = 2 × (1/SinA)

= 2 × (CosecA)

= 2CosecA

∴ LHS = RHS

Hence proved

Thus,

(SinA/(1 + CosA)) + ((1 + CosA)/SinA) = 2CosecA

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Hope it helped and believing you understood it........All the best