Question

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

Answer 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