# Mathematics

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

Thank you!

• Mathematics -

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 -

I got sqrt6/4 - sqrt2/4 for sin15 and sqrt6/4 + sqrt2/4 for cos15. Is it right?
Thank you!

• Mathematics -

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 -

OR

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

• Mathematics -

Thanks.

• Mathematics -

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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