precalculus

For each of the following determine whether or not it is an identity and prove your result.

a. cos(x)sec(x)-sin^2(x)=cos^2(x)

b. tan(x+(pi/4))= (tan(x)+1)/(1-tan(x))

c. (cos(x+y))/(cos(x-y))= (1-tan(x)tan(y))/(1+tan(x)tan(y))

d. (tan(x)+sin(x))/(1+cos(x))=tan(x)

e. (sin(x-y))/(sin(x)cos(y))=1-cot(x)tan(y)

f. sin(x)sin(y)=(1/2)[cos(x-y)-cos(x+y)]

asked by anonymous
  1. a
    1 - s^2 = c^2
    yes
    s^2+c^2 = 1

    b
    t(x+pi/4) = (t x + 1)/(1-t x)
    yes

    c
    t x t y = s x /c x * s y/c y
    so on the right we have
    [1 - (s x s y / c x c y) ] / [ 1 + ( s x s y /c x c y) ]

    [c x c y - s x s y] / [c x c y + s x s y]
    which is indeed
    c(x+y)/c(x-y)
    so yes

    d I am getting bored. I think you cn see the plan.

    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. Trig

    Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos
  2. Trigonometry desperate help, clueless girl here

    2. solve cos 2x-3sin x cos 2x=0 for the principal values to two decimal places. 3. solve tan^2 + tan x-1= 0 for the principal values to two decimal places. 4. Prove that tan^2(x) -1 + cos^2(x) = tan^2(x) sin^2 (x). 5.Prove that
  3. Trigonometry

    Please review and tell me if i did something wrong. Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot
  4. Trigonometry

    1.Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two decimal places. 6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin y 10.Prove that 1+tanθ/1-tanθ = sec^2θ+2tanθ/1-tan^2θ 17.Prove
  5. Mathematics - Trigonometric Identities

    Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) =
  6. trigonometry help me

    6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin y 10.Prove that 1+tanθ/1-tanθ = sec^2θ+2tanθ/1-tan^2θ 17.Prove that sin^2w-cos^2w/tan w sin w + cos w tan w = cos w-cot w cos w 23.Find a
  7. math

    Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of si -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using
  8. trig help much appreciated! :))

    1. Find the complete exact solution of sin x = . 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. 4. Prove
  9. Pre-calculus help

    I have two problems I am stuck on, if you could show me how to solve the problems it would be much appreciated. 1) Find sin 2x, cos 2x, and tan 2x from the given information. tan x = − 1/6, cos x > 0 sin 2x = cos 2x = tan
  10. math

    Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of sin -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using

More Similar Questions