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.
+128408 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 !!! ]
