If Cosec A+Cot A=4, find Sin A?

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answers:
Indica say: cosecA−cotA = (cosec²A−cot²A) / (cosecA+cotA) = 1/4
∴ 2cosecA = 4+1/4 = 17/4 ⟹ sinA = 8/17
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Como say: -
1/sinA + cosA/sinA = 4
1 + cos A = 4 sin A
sin A = (1/4) (1 + cos A)
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khalil say: 1/sina + cosa / sina = 4
1+ cosa = 4sina
2cos²(a/2) = 8 sin(a/2) cos(a/2)
if cos (a/2) is non-zero
cos(a/2) = 4 sin(a/2)
tan(a/2) = 1/4
cota = (1- tan²a/2) / 2tan(a/2)
cota = ( 1- 1/16) / (1/2) = 15/8
1+cot²a = 1/sin²a
1+ 225/64 = 1/ sin²a
sina = ±8/17
test the answers .... sina = 8/17 accepted
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az_lender say: 1/sin(A) + cos(A)/sin(A) = 4 =>
1 + cos(A) = 4*sin(A) =>
cos(A) = 4*sin(A) - 1 =>
cos^2(A) = 16*sin^2(A) - 8*sin(A) + 1 =>
1 - sin^2(A) = 16*sin^2(A) + 8*sin(A) + 1 =>
0 = 17*sin^2(A) + 8*sin(A) =>
0 = [sin(A)]*[17*sin(A) + 8].

The original equation indicates that sin(A) cannot be 0, so we conclude that
sin(A) = -8/17.
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crazy say: yes
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