Question

Prove that cot(a+15)-tan(a-15)=4cos2a/1+2sin2a

Answer 1

cot(A+15) - tan(A-15)

cos(A+15) / sin(A+15) - sin(A-15) / cos(A - 15)

[cos(A+15)cos(A-15) - sin(A-15)sin(A+15)] / [ sin(A+15)cos(A-15)

cos2A / sin(A+15)cos(A-15)

2cos2A / 2sin(A+15)cos(A-15)

2cos2A / [sin2A +sin30]

2cos2A / [ sin2A + 1/2]

2cos2A / [(2sin2A+1)/2]

4cos2A / (2sin2A + 1)
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Answer 2

Answer:

L. H. S

cot(A+15) - tan(A-15)

cos(A+15) / sin(A+15) - sin(A-15) / cos(A - 15)

[cos(A+15)cos(A-15) - sin(A-15)sin(A+15)] / [ sin(A+15)cos(A-15)

cos2A / sin(A+15)cos(A-15)

2cos2A / 2sin(A+15)cos(A-15)

2cos2A / [sin2A +sin30]

2cos2A / [ sin2A + 1/2]

2cos2A / [(2sin2A+1)/2]

4cos2A / (1+2sin2A)=R. H. S