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If x=5+2√6 and cosΦ=2√x / x-1, find the value of tan²Φ+cos²Φ

Guest Mar 7, 2017
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 #1
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Tan(x) =sqrt[1 - cos^2(x)] / cos(x)..............(1)

If x=5+2√6 and cosΦ=2√x / x-1, find the value of tan²Φ+cos²Φ

x =9.89898....., then: cos(0) =0.70710678.........and Tan(0) =1.

Cos^2(0) + Tan^2(0) =0.70710678^2 + 1^2 =0.5 + 1 =1.5

 

CPhill: Please verify this. Thanks.

Guest Mar 7, 2017
 #2
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cos^2(theta)   =  [4x] / (x - 1)^2  = 

 

4 [ 5 + 2sqrt(6)] / [ 4 + 2sqrt(6)] ^2  =

 

4 [5 + 2sqrt(6)]  / [ 2 (2 + sqrt(6) ] ^2 =

 

[ 5 + 2sqrt(6) ] / [ 2 + sqrt(6)]^2  =

 

[5 + 2sqrt(6)] / [ 4 + 4sqrt(6) + 6] =

 

[5 + 2sqrt(6)] / [ 10 + 4sqrt(6)] =

 

[5 + 2sqrt(6)] / [2 (5 + 2sqrt(6) ) ] =   1/2

 

And 

 

sin^2(theta) = 1 - cos^2(theta)  =  1 - 1/2  = 1/2

 

So

 

tan^2(theta) + cos^2(theta)  =

 

sin^2(theta) /cos^2(theta) + cos^2(theta)  =

 

[1/2] / [1/2] + 1/2  =

 

1 + 1/2  =

 

3/2         [ Correct, Guest !!! ]

 

 

cool cool cool

CPhill  Mar 7, 2017

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