# If tan A + sec A = 4 how do you find the value of cos A?

Oct 14, 2015

Multiply both sides with $\cos x$ we get

$\tan A + \sec A = 4 \implies 1 + \sin A = 4 \cos A$

Square both sides in the last one

1+2sinA+sin^2A=16cos^2A=> 1+2sqrt(1-cos^2A)=16cos^2A-(1-cos^2A)=> 2sqrt(1-cos^2A)=17cos^2A-2

Solving $2 \sqrt{1 - {\cos}^{2} A} = 17 {\cos}^{2} A - 2$ with respect to $\cos A$ we get

$\cos A = \pm \frac{8}{17}$