Question

prove that
cot (A+15°) - tan (A-15°) = 4cos 2A / 1+2 sin 2A
​

Answer 1

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