# Math

Prove that (cos2A)÷ ( 1+sin2A) = (cotA -1) ÷ (cotA +1)

1. 👍 0
2. 👎 0
3. 👁 859
1. The trick here is to recall that 1 = cos^a+sin^2A

cos2A/(1+sin2A)
(cos^2A-sin^2A)/(1+2sinAcosA)
(cos^2A-sin^2A)/(cos^2A+2sinAcosA+sin^2A)
(cosA+sinA)(cosA-sinA)/(cosA+sinA)^2
(cosA-sinA)/(cosA+sinA)
(cotA-1)/(cotA+1)

1. 👍 0
2. 👎 0
2. The trick here is to recall that 1 = cos^a+sin^2A

cos2A/(1+sin2A)
(cos^2A-sin^2A)/(1+2sinAcosA)
(cos^2A-sin^2A)/(cos^2A+2sinAcosA+sin^2A)
(cosA+sinA)(cosA-sinA)/(cosA+sinA)^2
(cosA-sinA)/(cosA+sinA)
(cotA-1)/(cotA+1)

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Trigonometry

If A + B + C = 180°, Prove that Cos²A + Cos²B + Cos²C = 1-2cosAcosBcosC

2. ### maths

Prove SinA/1-CosA = CosecA + CotA

3. ### maths

Prove that [1+cotA-CosecA] [1+tanA+secA] = 2

4. ### Math

For the function f(x)=sinx, show with the formula sin^2A=1/2(1-cos2A) that f(x+y)-f(x)=cosxsiny-2sinxsin^2(1/2y)

1. ### math

cos^6A-sin^6A=cos2A(1-1÷4sin^2 2A) Prove

2. ### Inverse trigonometry

Prove that- tan^-1(1/2tan 2A)+tan^-1(cotA)+tan^-1(cot^3A) ={0,ifpi/4

3. ### Maths

Prove sqrt(Sec^2 A+Cosec^2 A)=TanA+CotA

4. ### Maths

Express cosA in terms of cotA

1. ### maths

Prove that in any triangle ABC Sin2A+Sin2B+Sin2C/SinA+SinB+SinC=8Sin(A/2)Sin(B/2)Sin(C/2)

2. ### Trigonometry

cos²a + cos²(a+120°) + cos(a-120°) = 3/2

3. ### Trig

How do you express sin4x as a trigonometric funcition of x using the identities? I think that you are supposed to start with the sine sum identity and then use the double angle identities for sin2A and cos2A, but after that I get

4. ### Trigonometry

Prove that sin(n+1)Asin(n-1)A + cos(n+1)Acos(n-1)A = cos2A