Asked by Anonymous

How can I evaluate the expression below without using calculator?
cos15*2sin15

Thank you!
Answered by Emileee
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
Answered by 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!
Answered by 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.
Answered by Reiny
OR

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