1. ## trigonometric identites

I need help on this question:

Q) Calculate without using a calculator the exact value of
√3 cos15 - sin15

Ans) √2

can someone show me the working of it. Thx!

(the equation isnt equal to 0 or anything)

2. Originally Posted by Sundae
I need help on this question:

Q) Calculate without using a calculator the exact value of
√3 cos15 - sin15

Ans) √2

can someone show me the working of it. Thx!

(the equation isnt equal to 0 or anything)
Use the half angle formulas: 4. Half Angle Formulas

3. The half angle formula hasnt been introduced in the chapter yet, only the addition formula so i dont think im suppose 2 use it for this question. (and i dont know where to begin wiv tht formula).

4. Originally Posted by Sundae
I need help on this question:

Q) Calculate without using a calculator the exact value of
√3 cos15 - sin15

Ans) √2

can someone show me the working of it. Thx!

(the equation isnt equal to 0 or anything)
Originally Posted by Sundae
The half angle formula hasnt been introduced in the chapter yet, only the addition formula so i dont think im suppose 2 use it for this question. (and i dont know where to begin wiv tht formula).
cos(15) = cos(45 - 30)

sin(15) = sin(45 - 30)

5. that just made things more muddled up... buh thx for ur help.

6. Originally Posted by Sundae
that just made things more muddled up... buh thx for ur help.
What have you covered already? As far as I'm aware the two solutions proposed by Mr F are the best/only methods:

$\displaystyle cos(A \pm B) = cosAcosB \mp sinAsinB$

$\displaystyle sin (A \pm B) = sinAcosB \pm cosAsinB$

unless you're more familiar with that form.
(The half angle formulae are also derived from that form because cosA = cos(0.5A+0.5A))

7. im using the heineman c3 book, exercise 7A its only covered the additional rule.

8. Originally Posted by Sundae
im using the heineman c3 book, exercise 7A its only covered the additional rule.
If you are unable to apply either of the methods I have suggested then you are currently not in a position to be able to do the question at all. In which case you will just have to wait until you have covered that material in class. Then come back and review this thread.

9. i home school >.< i dont have a teacher i been teaching myself.

10. Originally Posted by Sundae
i home school >.< i dont have a teacher i been teaching myself.
Then find the section of your book that has the fomulas given in post #6. Then review this thread. There's no point trying attempting questions that require maths you haven't learned or studied.

11. i understand what ur saying, i appreciate ur help. I just wanted to see the working out of the question >.<