Mathematics
posted by Anonymous on .
How can I evaluate the expression below without using calculator?
cos15*2sin15
Thank you!

you can use the sum and difference rules
cos15 = cos (4530) = cos45*cos30 + sin45*sin30
sin15 = sin (4530) = sin45*cos30  cos45*sin30
45 and 30 are the common trig values to know 
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! 
Also, can you give me the exact formulas for the sum and difference rules (both sin and cos) without substituting any angles there? Thanks.

OR
cos15*2sin15
= 2(sin15)(cos15)
= sin 30
= 1/2 
How did you do this, Reiny? I don't understand. How does 2(sin15)(cos15) equal sin30? Please help!
Thanks. 
the "halfangle" formula
sin 2A = 2(sinA)(cosA)
in this case A = 15ยบ
by the way, you can check on a calculator
your (cos15)(2sin15) = .5 or 1/2