PreCalc
posted by Alyssa
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

Reiny
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 30690 triangle
2) same suggestion, you must know these formulas
sin(AB) = 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
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