Question

Verifying an equation

Answer 1

\[\sin(x+\frac{ \pi }{ })−\cos(x+\frac{ \pi }{ 3 })=\sqrt{3}sinx\]

Answer 2

Can you please help me. I don't know my next step

Answer 3

oh crapp

Answer 4

its pi/6

Answer 5

\[\[\sin(x+\frac{ \pi }{ 6 })−\cos(x+\frac{ \pi }{ 3 })=sqroot(3) sinx\]\]

Answer 6

If you want to solve for x, expand the left hand side using the trig identity:
sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
cos(A+B) = cos(A)cos(B) - sin(A)sin(B)

Answer 7

okok let me do that

Answer 8

ok

Answer 9

so now i find all the exact values that I can get?

Answer 10

Well they are not asking you to solve the equation but just to verify.
If you expand the left hand side and simplify you will notice it becomes sqrt(3)sin(x).

Answer 11

to simplify would i need to find some of the exact values ? because theres nothing i can do after expanding the LHS

Answer 12

well i don't see anything*

Answer 13

You can substitute the values for sin(pi/6), cos(pi/6), sin(pi/3), cos(pi/3) from the unit circle or trig tables.

Answer 14

ahhh ok that's what I meant. let me do that :p

Answer 15

im left with \[sinx \frac{ \sqrt{3} }{ 3 } - sinx \frac{ \sqrt{3} }{ 2 }\]

Answer 16

It should be \[\frac{ \sqrt(3) }{ 2 }\sin(x) + \frac{ \sqrt(3) }{ 2 }\sin(x) = \sqrt(3)\sin(x)\]

Answer 17

oh whoopesies I replaced the 2 with a 3

Answer 18

wait so sqroot3/2, where does the two go in the equation??? The denominator

Answer 19

\[\frac{ \sqrt(3) }{ 2 }\sin(x) + \frac{ \sqrt(3) }{ 2 }\sin(x) = 2 * \frac{ \sqrt(3) }{ 2 }sin(x) = \sqrt(3)\sin(x)\]

Answer 20

i don't understand how they merge

Answer 21

Not squared. Here we are ADDING two fractions. Not multiplying.

If we are multiplying two identical terms we can square it. But when we are adding two identical terms we need to multiply by 2 or double it (not square it).

Answer 22

ahhh

Answer 23

5 + 5 = 2 * 5 = 10
a + a = 2 * a = 2a
1/4 + 1/4 = 2 * 1/4 = 1/2

Answer 24

since we are adding fraction with fraction

Answer 25

wow xD that was dumb of me. it was just because everything is like in big numbers

Answer 26

So we get sqrt(3) * sin(x) which is the right hand side. So we have verified what was asked.