trigonometry

Verify that following are identities:


1. cos 3t = 4 cos³ t-3 cos t

2. sin 4x = 8 sin x cos³ x-4 x cos x

(use a double-angle identity)

asked by PDF
  1. 1.
    LS = cos 3t
    = cos(2t + t)
    = cos2tcost - sin2tsint
    = (2cos^2 t - 1)(cost) - 2sintcostsint
    = 2cos^3 t - cost - 2sin^2 t cost
    = 2cos^3 t - cost - 2(1 - cos^2 t)cost
    = 2cos^3 t - cost - 2cost + 2cos^3 t
    = 4cos^3 t - 3cost
    = RS

    for #2, start with
    LS = sin(2x + 2x)
    = sin2xcos2x + cos2x sin2x
    then use the double-angle formulas for each one
    simplify very carefully

    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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) =
  2. TRIG!

    Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x +
  3. verifying trigonometric identities

    How do I do these problems? Verify the identity. a= alpha, b=beta, t= theta 1. (1 + sin a) (1 - sin a)= cos^2a 2. cos^2b - sin^2b = 2cos^2b - 1 3. sin^2a - sin^4a = cos^2a - cos^4a 4. (csc^2 t / cot t) = csc t sec t 5. (cot^2 t /
  4. Trig!

    The identities cos(a-b)=cos(a)cos(b)sin(a)sin(b) and sin(a-b)=sin(a)cos(b)-cos(a)sin(b) are occasionally useful. Justify them. One method is to use rotation matricies. Another method is to use the established identities for
  5. trig

    it says to verify the following identity, working only on one side: cotx+tanx=cscx*secx Work the left side. cot x + tan x = cos x/sin x + sin x/cos x = (cos^2 x +sin^2x)/(sin x cos x) = 1/(sin x cos x) = 1/sin x * 1/cos x You're
  6. Mathematics - Trigonometric Identities - Reiny

    Mathematics - Trigonometric Identities - Reiny, Friday, November 9, 2007 at 10:30pm (sinx - 1 -cos^2x) (sinx + 1 - cos^2x) should have been (sinx - 1 + cos^2x) (sinx + 1 - cos^2x) and then the next line should be sin^2x + sinx -
  7. Math(Please check)

    Use the fundamental identities to simplify the expression. tan^2 Q / sec^2 Q sin^2/cos^2 / 1/cos^2 = sin^2 / cos^2 times cos^2 / 1 = The cos^2 cancels out so sin^2 is left. Is this correct?
  8. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b)
  9. trig

    Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The
  10. Math

    Prove the identities 1. cos3Ɵ + cos Ɵ = 4cos^Ɵ - 2 cos Ɵ 2. sin (A+B)sin (A-B)=cos2B + sin^2 A-1

More Similar Questions