I figured this out using my calculator but I need help solving through it without.

(cosX)/(1+sinX)+tanX

I figured this out using my calculator but I need help solving through it without.

(cosX)/(1+sinX)+tanX

Tutors, please sign in to answer this question.

Westford, MA

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).

Flemington, NJ

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)

the answer would be:

1/cosX

Rachim B.

Experienced, enthusiastic, patient.

Cliffside Park, NJ

4.5
(28 ratings)

Daniel H.

Harvard & Law School Graduate - Master Tutor for Tests/Academics

New York, NY

4.9
(45 ratings)

John P.

Math, Science, Technology, and Test Prep Tutor

Fort Lee, NJ

5.0
(668 ratings)

- Trigonometry 1327
- Trigonometric Functions 193
- Math Help 4840
- Trig 163
- Math 8574
- Precalculus 1416
- Trig Identities 48
- Identities 26
- Trigonometric Formulas 23
- Cosine 81