If sec0-tan0=4

Question

Then prove that cos0= 8/7

Answer 1

Clearly you have a typo, since cosine is never greater than 1.

secθ-tanθ = 4
Since we want cosθ at the end, let's change stuff now:

1/cosθ - sinθ/cosθ = 4
(1-sinθ) = 4cosθ
1-2sinθ+sin^2θ = 16-16sin^2θ
17sin^2θ-2sinθ-15 = 0
(15sinθ-17)(sinθ+1) = 0
sin17sin^2θ-2sinθ-15 = 15/17 or -1

So, cosθ = 8/17

The other angle is a spurious solution