+0

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

0
63
2

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

Guest Mar 7, 2017
Sort:

#1
0

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

Guest Mar 7, 2017
#2
+76821
0

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 !!! ]

CPhill  Mar 7, 2017

### 16 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details