Pre-Calc

I am really struggling with how to do these problems, I posted them a few minutes ago but the answers/work shown was incorrect.

1)
a) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.

cos 12° cos 18° − sin 12° sin 18°

b) And Find its exact value.

2)
a)Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.

sin 4pi/5 cos 7pi/15 - cos 4pi/5 sin 7pi/15

b) And find its exact value.

3)

Write the trigonometric expression in terms of sine and cosine, and then simplify.

tan θ / cos θ − sec θ

asked by Alyssa
  1. You must make an effort to memorize the formulas.
    (I suggest you memorize the pattern)
    cos(A+B) = cosAcosB - sinAsinB
    Notice you have that pattern in
    cos 12° cos 18° − sin 12° sin 18°
    = co(12+18)
    = cos 30
    which you should have memorized as √3/2 from the 30-6-90 triangle

    2) same suggestion, you must know these formulas
    sin(A-B) = sinAcosB - cosAsinB
    then sin 4pi/5 cos 7pi/15 - cos 4pi/5 sin 7pi/15
    = sin(4π/5 - 7π/15)
    = sin((1/3)π) or sin π/3 or sin 60°
    again you should know that one
    sin π/3 = √3/2

    3
    tanØ/cosØ - secØ
    = (sinØ/cosØ) / cosØ - 1/cosØ
    = sinØ/cos^2 Ø - cosØ/cos^2 Ø
    = (sinØ - cosØ)/cos^2 Ø

    posted by Reiny

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