We have to solve (tan x)^2 = 8 - 8*sec x.
(tan x)^2 = 8 - 8*sec x
=> (sin x)^2 / (cos x)^2 = 8 - 8/(cos x)
=> (1 - (cos x)^2) / (cos x)^2 = (8*(cos x)^2 - 8* cos x)/ (cos x)^2
=> (1 - (cos...
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We have to solve (tan x)^2 = 8 - 8*sec x.
(tan x)^2 = 8 - 8*sec x
=> (sin x)^2 / (cos x)^2 = 8 - 8/(cos x)
=> (1 - (cos x)^2) / (cos x)^2 = (8*(cos x)^2 - 8* cos x)/ (cos x)^2
=> (1 - (cos x)^2) = (8*(cos x)^2 - 8* cos x)
=> 9(cos x)^2 - 8 cos x - 1 = 0
=> 9(cos x)^2 - 9 cos x + cos x - 1 = 0
=> 9(cos x)(cos x - 1) + 1( cos x - 1) = 0
=> (9(cos x) - 1)(cos x - 1) = 0
cos x = 1 and cos x = 1/9
x = arc cos 1 and x = arc cos (1/9) and - arc cos (1/9)
The required values are : x = 2*n*pi and x = arc cos (1/9) + 2*n*pi and x = -arc cos (1/9) + 2*n*pi