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If tan A = 1 - cos B/sin B show that tan 2A = tan B.

If tan A = 1 - cos B/sin B show that tan 2A = tan B.

Grade:12th pass

3 Answers

Akash
50 Points
6 years ago
TanA =2sin2 (B/2)/2sin(B/2)cos(B/2) =tan(B/2) now :- tan2A =2tan(A)/1-tan2(A) = 2tan(B/2)/1-tan2(B/2) = tan2 B/2 = tanB. Hence it is proved.
Rakshita
13 Points
5 years ago
Change all into sin and cos function
Sin A sin B = cos A – cos A cos
Cos (B-A) we easily get that 
B-A = AB = 2A, tan 2A = tan B
 
Mehul Kochar
30 Points
4 years ago
TanA=1-CosB/SinB
Tan2A=2TanA/1-Tan2A
=2(1-CosB)/SinB/1-(1-CosB)2/Sin2B
=2(1-CosB)SinB/Sin2B-1-Cos2B+2CosB
=2(1-CosB)SinB/2CosB-Cos2B-1
=2SinB(1-CosB)/2CosB-(1+Cos2B)
=2SinB(1-CosB)/2CosB-2Cos2B
=2SinB(1-CosB)/2CosB(1-CosB)
=TanB..........Hence Proved

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