MoDULE 4: TrIGONOMETRY IDENTITY PRoJECT OVERVIEw We will apply the concepts and

Question

MoDULE 4: TrIGONOMETRY IDENTITY PRoJECT OVERVIEw We will apply the concepts and formulas of evaluating trigonometric identities to complete this project INSTRUCTIONS You have been asked to use your skills with identities to solve a few trigonometric crimes that have recently occurred in your area. You can choose between solving all cases 1-4 OR only case 5. You should compilea report detailing your work for each case. For each case, you should clearly identify and explain all steps involved in your solutions. Your completed report should be presented in a professional manner and submitted directly to the drop box. Late submissions will not be accepted. Good luck on your mission!

Explanation / Answer

case1,

cscx - cotx = (1/sinx) - (cosx/sinx) = (1 - cosx)/sinx = (1-cosx)(1+cosx)/sinx(1+cosx)

= (1-cos2x)/sinx(1+cosx) = sin2x/sinx(1+cosx) = sinx/(1+cosx)

case2,

1/(1 - cotx) = 1/(1 - (cosx/sinx)) = 1/((sinx - cosx)/sinx) = sinx/(sinx - cosx)

case3,

cotx(cosxtanx + sinx) = (cosx/sinx)(cosx(sinx/cosx) + sinx) = (cosx/sinx)(sinx + sinx) = 2cosx

case4,

csc4x - cot4x = csc4x - (cot2x)2 = csc4x - (csc2x - 1)2 = csc4x - (csc4x + 1 - 2csc2x) = 2csc2x - 1

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