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If tan(a-b) =cot b, then how to find sin(a-b) and cos(a-b)

If tan(a-b) =cot b, then how to find sin(a-b) and cos(a-b)

Grade:12th pass

4 Answers

Arun
25750 Points
6 years ago
Dear student
sin (a-b)/cos (a-b) = cos b/ sin b
sin (a-b) sin b - cos b cos(a-b) = 0
- cos (a-b+b) = 0
Cos a = 0
a = 90°
Hence
sin(90- b) = cos b
Cos (90 -b) = sin b
Regards
Arun (askIITians forum expert)
Lucky
27 Points
6 years ago
tan(b)tan(a-b)= 1. So 1-tan(b)tan(a-b) =0So tan(b + (a-b)) = (tanb + tan (a-b))/ 1- tan(b)tan(a-b). So from putting value of denominator we get tan( b+(a-b)) = infinitySo a= 90 . So sin(90-b) = cosb and cos (90-b)= Sinb.
Satyam Kumar
39 Points
6 years ago
tan(a-b)=cotbtan(a-b)=tan(90-b)a-b=90-b:.a=90°:.sin(90-b)=cos b and cos(90-b)=sin bIdentity used:sin(90-a)=cos a cos(90-a)=sin a cot(90-a)=tan a
Satyam Kumar
39 Points
6 years ago
tan(a-b)=cotb.......tan(a-b)=tan(90-b).......a-b=90-b:.a=90°.......:.sin(90-b)=cos b and cos(90-b)=sin b....... Identity used:sin(90-a)=cos a .......cos(90-a)=sin a....... cot(90-a)=tan a......

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