Posted by **Anonymous** on Wednesday, May 20, 2009 at 8:28pm.

How can I evaluate the expression below without using calculator?

cos15*2sin15

Thank you!

- Mathematics -
**Emileee**, Wednesday, May 20, 2009 at 9:41pm
you can use the sum and difference rules

cos15 = cos (45-30) = cos45*cos30 + sin45*sin30

sin15 = sin (45-30) = sin45*cos30 - cos45*sin30

45 and 30 are the common trig values to know

- Mathematics -
**Anonymous**, Wednesday, May 20, 2009 at 10:00pm
I got sqrt6/4 - sqrt2/4 for sin15 and sqrt6/4 + sqrt2/4 for cos15. Is it right?

And the answer would be 6radical3/4???

Thank you!

- Mathematics -
**Anonymous**, Wednesday, May 20, 2009 at 10:07pm
Also, can you give me the exact formulas for the sum and difference rules (both sin and cos) without substituting any angles there? Thanks.

- Mathematics -
**Reiny**, Wednesday, May 20, 2009 at 10:45pm
OR

cos15*2sin15

= 2(sin15)(cos15)

= sin 30

= 1/2

- Mathematics -
**Anonymous**, Wednesday, May 20, 2009 at 11:10pm
How did you do this, Reiny? I don't understand. How does 2(sin15)(cos15) equal sin30? Please help!

Thanks.

- Mathematics -
**Reiny**, Wednesday, May 20, 2009 at 11:14pm
the "half-angle" formula

sin 2A = 2(sinA)(cosA)

in this case A = 15º

by the way, you can check on a calculator

your (cos15)(2sin15) = .5 or 1/2

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