Question

If cosecA=2 find the value of cotA+sinA/1+cosA​

Answer 1

sol:

CosecA = 2

Sin A = 1/2

cos²A + sin²A = 1

cos²A + (1/2)² = 1

cos²A + 1/4 = 1

1 - 1/4 = cos²A

cos²A = 3/4

cosA = √(3)/2

TanA = sinA/CosA = 1/2 × 2/√(3)

TanA = 1/√(3)

CotA = √(3)

Now,

cotA+sinA/1+cosA

= √(3) + 1/2 / 1 + √(3)/2

= 2√(3) + 1/2 / 2 + √(3)/ 2

= 2√(3) + 1/2 × 2/2 + √(3)

= [2√(3) + 1] × [2 + √(3)]

= 2[2√(3) + 1] + √(3)[2√(3) + 1]

= 4√(3) + 2 + (2×3) + √(3)

= 5√(3) + 2 + 6

= 5√(3) + 8 is the value.