cos(1/2 tan^-1 3/5)=

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cos(1/2 tan^-1 3/5)=

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Answer 1

Hi  Sandra,

For finding any trig function when the question is mix of function and its inverse you need to be very

CAREFUL. Follow me 

cos(1/2 tan^-1 3/5)=?

1/2 tan^-1 3/5 = α α = angle In fact we need to find cos(α) = ?

both side times 2

tan^-1 3/5 = 2α

3/5 = tan2α it is very important you use the definition of tangent ( tangent = opp / adj )

opp = 3 and adj = 5 as a result r^2 = 3^2 + 5^2 = 9 + 25 = 34 ---> r = √34 = hyp

on the other hand, 3/5 = tan2α ----> cos2α = adj / hyp = 5/√34

cos2α = 5/√34 now you have cos2α and you need to find cos (α)

We know cos 2α = 2 cos² α - 1 bu replacing cos 2α you can find cosα

5/√34 = 2 cos² α - 1 both side add 1

1 + 5/√34 = 2 cos²a both side divide by 2

1/2( 1 + 5/√34 )= cos²α root of the both side

√ [ 1/2( 1 + 5/√34 )] = cosα

I hope it is useful,

Minoo

Answer 2

cos(1/2 tan^-1 3/5)= .964