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

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

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Answer 1 · 2015-10-14T21:38:47

Multiply both sides with $cos x$ $cosx$ we get

$tan A + sec A = 4 \Rightarrow 1 + sin A = 4 cos A$ $tanA+secA=4=>1+sinA=4cosA$

Square both sides in the last one

$1 + 2 sin A + {sin}^{2} A = 16 {cos}^{2} A \Rightarrow 1 + 2 \sqrt{1 - {cos}^{2} A} = 16 {cos}^{2} A - (1 - {cos}^{2} A) \Rightarrow 2 \sqrt{1 - {cos}^{2} A} = 17 {cos}^{2} A - 2$ $1+2sinA+sin^2A=16cos^2A=> 1+2sqrt(1-cos^2A)=16cos^2A-(1-cos^2A)=> 2sqrt(1-cos^2A)=17cos^2A-2$

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

$cos A = \pm \frac{8}{17}$ $cosA=+-8/17$

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

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

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