Question

Cos^2a = sin^3a , so what is the value of tan^6a-tan^2a

Answer 1

Answer:

Step-by-step explanation:

Given that

cosA, sinA, cotA are in G.P

=> sin2 A = cosA*cotA

= (cosA*cosA)/sinA

=> sin2 A = cos2 A/sinA

=> sin2 A/cos2 A = 1/sinA

=> tan2 A = 1/sinA

Now tan6 A - tan2 A

= (tan2 A)3 - tan2 A

= (1/sinA)3 - 1/sinA

= 1/sin3 A - 1/sinA

= (1-sin2 A)/sin3 A

= cos2 A/sin3 A

= cot2 A*cosecA

= (cosA/sinA)2 * (1/sinA)

= cot2 A*cosecA

So tan6 A - tan2 A = cot2 A*cosecA