Question

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

Answer 1

Multiply both sides with `cosx` we get

`tanA+secA=4=>1+sinA=4cosA`

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 `2sqrt(1-cos^2A)=17cos^2A-2` with respect to `cosA` we get

`cosA=+-8/17`