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# Trigonometry

I figured this out using my calculator but I need help solving through it without.
(cosX)/(1+sinX)+tanX

### 2 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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Calculators only give approximate answers, no matter how many decimals you get from it. They can serve as guides, but only an analytic method will get exact answers.

Let's use the alternative technique in:

cos(θ)/(1+sin(θ))+tan(θ) =

(x/r)/(1 + y/r) + y/x =

x/(r + y) + y/x =

x*x/(x*(r + y)) + y*(r + y)/(x*(r + y)) =

(x*x + y*(r + y))/(x*(r + y)) =

(x^2 + yr + y^2)/(x*(r + y)) =

(r^2 + yr)/(x*(r + y)) =

r(r + y)/(x*(r + y)) =

r/x = 1/cos(θ) = sec(θ).
Mozhgan Z. | Professional Math, Chemistry and Physics TutorProfessional Math, Chemistry and Physics...
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cosX/(1+sinX)+tanX

we know that: tanX=sinX/cosX, therefore:

cosX/(1+sinX)+sinX/cosX

common denominator would be cosX(1+sinX), so the addition of these two terms would be:

(cosX^2+sinX+sinX^2)/cosX(1+sinX)

knowing sinX^2+cosX^2=1, we'll have:

(1+sinX)/cosX(1+sinX)

cancel out (1+sinX)