how do u evaluate sin75+cos75 without tables?

Question

the soln. given was:

sin 75+ cos(90-15)
sin 75+ sin 15
2sin45 * cos 30

i don't get the last step

pls. explain it to me

Answer 1

Baby, this is an advanced Trigonometric relation which basically states that

sin A + sin B = 2 sin (A+B)/2 x cos (A-B)/2

One more

cos A + cos B = 2 cos (A+B)/2 x cos (A-B)/2

There are two more:

sin A + cos B
cos A - cos B

Look into your Math book, and you'll definitely find these formulas, as they are very standard in usage,, trust me.

Answer 2

sin (45+30)+ cos(45+30)
use the formula sin(A+B) =sin A cos B+cos A sin B
and cos(A+B) = cos A cos B -Sin A SinB
sin(45+30) =sin 45 cos 30+cos 45 sin 30
sin(75) =(1/sq rt 2)(sq rt 3/2)+(1/sq rt 2)(1/2).................i
cos(45+30) = cos 45 cos 30 -Sin 45 Sin30
cos 75 =(1/sq rt 2)(sq rt 3/2) -(1/sq rt 2)(1/2).................ii
Add i and ii we get
sin75+cos75 =2(1/sq rt 2)(sq rt 3/2)=sq rt(3/2)

Answer 3

there is an identitie that says:

sin(s) + sin(t) = 2 sin((s+t)/2)cos((s-t)/2)

sin(75) + sin(15) = 2 sin((75 + 15)/2)cos((75-15)/2)
sin(75) + sin(15) = 2 sin(45)cos(30)

http://www.clarku.edu/%7Edjoyce/trig/identities.html

if you want an extra refference for trig I really like this http://www.clarku.edu/%7Edjoyce/trig/

Answer 4

you can say

sinA+sinB=
2 sin(A+B)/2 Cos (A-B)/2
so you get
2 sin 45 *cos 30

Answer 5

cant you do it on your calculator.