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Grade: 12th pass
        If tan(a-b) =cot b, then how to find sin(a-b) and cos(a-b)
7 months ago

Answers : (4)

Arun
12307 Points
							
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)
7 months ago
Lucky
27 Points
							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.
						
7 months ago
Satyam Kumar
39 Points
							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
						
5 months ago
Satyam Kumar
39 Points
							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......
						
5 months ago
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