Question

Help me solve:
sin(x + (π / 4)) – sin(x – (π / 4) = 1

Answer 1

hey look at this diagram

Answer 2

Okay

Answer 3

or else use the formula of
\(\huge\color{red}{\tt sin(A-B)~and~sin(A+B)}\)

Answer 4

do you know those formulas ?

Answer 5

These are the addition and subtraction trig formulas for sine right?

Answer 6

yes
use them and expand the LHS

Answer 7

LHS??? What's that

Answer 8

Left Hand Side

Answer 9

This is gonna take a while to type so hold on..

Answer 10

Take your time :)

Answer 11

sin ( a+b) = sin x cos (pi/4) + cos x sin (pi/4)
sin (a - b) = -sin x cos (-pi/4) - cos x sin (pi/4)

Answer 12

I already accounted for the "-sin" in the equation found in my question

Answer 13

what sinx?
ohh
\(\Large(sin x cos (\pi/4) + cos x sin (\pi/4)\)\(\huge - \) \(\Large(sin x~ cos (-\pi/4) - cos x sin (\pi/4))\)

Answer 14

So what's next?

Answer 15

Saw something different i wrote?

Answer 16

@Shorty1234 ?

Answer 17

I'm confused...what are you talking about? @rvc

Answer 18

Well the brackets are important
when you open the brackets the sign changes
you did not add the brackets

Answer 19

Oh okay but we basically wrote the same thing except I didn't put the bracket in between "-" and "sin". So what's next?

Answer 20

yeah
so now open the brackets
what do you get?

Answer 21

What I wrote down the first time, right?

Answer 22

be careful about the signs