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

Mathematics 
Emileee,
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 
Mathematics 
Anonymous,
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,
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,
OR
cos15*2sin15
= 2(sin15)(cos15)
= sin 30
= 1/2 
Mathematics 
Anonymous,
How did you do this, Reiny? I don't understand. How does 2(sin15)(cos15) equal sin30? Please help!
Thanks. 
Mathematics 
Reiny,
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