Precal nightmare

Show that: sec (A-B)= (cos(A+B))/(cos^2 A-Sin^2 B)

  1. 👍 0
  2. 👎 0
  3. 👁 62
asked by krista
  1. LS
    = 1/cos(A-B)
    = 1/(cosAcosB + sinAsinB)
    multiply top and bottom by cosAcosB - sinAsinB
    = (cosAcosB - sinAsinB)/(cos^2Acos^2B - sin^2Asin^2B)
    = (cosAcosB - sinAsinB)/((1-sin^2A)(1-sin^2B) - sin^2A(sin^2B))
    = (cosAcosB - sinAsinB)/(1 - sin^2B - sin^2A + sin^2Asin^2B - sin^2Asin^2B)
    = cos(A+B)/(cos^2A - sin^2B)
    = RS

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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 +

    asked by hayden on February 23, 2009
  2. math

    How would you establish this identity: (1+sec(beta))/(sec(beta))=(sin^2(beta))/(1-cos(beta)) on the right, sin^2 = 1-cos^2, that factor to 1-cos * `1+cos, then the denominator makes the entire right side 1+cosB which is 1+1/sec

    asked by michelle on June 13, 2007
  3. MATH

    Hi, I really need help with these questions. I did some of them halfway, but then I got stuck. Would you please help me? Thank you so much. Prove the identity.... 1. sec x + tan x(1-sin x/cos x)=1 1/cos x + sin x/cos x(cos^2 x/cos

    asked by LIZZIE010 on January 2, 2014
  4. 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)

    asked by Pablo on November 26, 2006
  5. algebra

    Can someone please help me do this problem? That would be great! Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2

    asked by Valerie on February 18, 2007
  6. 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

    asked by Suzy on August 16, 2013
  7. 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

    asked by Paul C on November 26, 2006
  8. 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 that sin^2w-cos^2w/tan

    asked by Alonso on January 1, 2013
  9. pre-cal

    Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x

    asked by ethan on May 17, 2007
  10. 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?

    asked by Hannah on March 5, 2010
  11. 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) =

    asked by Anonymous on November 8, 2007

More Similar Questions