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

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Answer 1 · 2015-10-14T21:38:47

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

$cosA=+-8/17$

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