Use half angle identity to evaluate exactly cos pi8 Prove th

Use half- angle identity to evaluate exactly cos pi/8 Prove the identity cos (u - v)/cos u sin v = tan u + cot v

Solution

10)cos(A)=[(1+cos(2A))_/2]

cos(_/8)=[(1+cos(2_/8))_/2]

cos(_/8)=[(1+cos(_/4))_/2]

cos(_/8)=[(1+(1_/2))_/2]

cos(_/8)=[(2 +1)_/(22)]

cos(_/8)=[(2 +1)2_/(2*2)]

cos(_/8)=[(2 +2)_/4]

cos(_/8)=((2 +2))_/2

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11)cos(u-v)_/cosusinv

=[cosucosv +sinusinv]_/cosusinv

=(cosucosv_/cosusinv) +(sinusinv_/cosusinv)

=(cosv_/sinv) +(sinu_/cosu)

=cotv +tanu

=tanu +cotv