How can I evaluate the expression below without using calculator?

Question

cos15*2sin15

Thank you!

Answer 1

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

Answer 2

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!

Answer 3

Also, can you give me the exact formulas for the sum and difference rules (both sin and cos) without substituting any angles there? Thanks.

Answer 4

OR

cos15*2sin15
= 2(sin15)(cos15)
= sin 30
= 1/2

Answer 5

How did you do this, Reiny? I don't understand. How does 2(sin15)(cos15) equal sin30? Please help!
Thanks.

Answer 6

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