SOLUTION: If A is an angle such that tanA+secA=2, evaluate cosA.

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Question 1113584: If A is an angle such that tanA+secA=2, evaluate cosA.
Found 3 solutions by stanbon, ikleyn, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
If A is an angle such that tanA+secA=2, evaluate cosA.
-----
(sin/cos)+(1/cos) = 2
2*cos = (sin + 1)
cos(A) = (sin(A)+1)/2
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Cheers,
Stan H.
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Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.
 +  = 2


sin(A) + 1 = 2*cos(A)     =====>   Square both sides  ====>


 = .


Introduce new variable t = sin(A). Then your last equation becomes


 = 


 = 0


 =  = 


 =  =  =  = 0.6.


 =  = -1.


Thus sin(A) = 0.6  or -1.  Then EITHER  cos(A) =  +/-  = +/- 0.8   OR  cos(A) = 0.


The original equation excludes  cos(A) = 0.  It leaves only two opportunities for cos(A):  It is EITHER  0.8  OR  -0.8.


Easy check with the original equation shows that only value cos(A) = 0.8 works.  Value cos(A) = -0.8 does not work.


Answer.  cos(A)  is   0.8.


The plot below CONFIRMS this answer:






Plot y =  (red), y = 2 (green) and y = cos(x)

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Writing by  @stanbon  is not the solution of the problem.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
If A is an angle such that tanA+secA=2, evaluate cosA.




 -------- Squaring each side of equation

 ----- Substituting 



4 sec A = 5



 

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