Question

solve cosx + sinx = cos2x +sin2x

Answer 1

So what do plan to do, what are you thoughts to start solving this?

Answer 2

simplify cos2x and sin2x ?

Answer 3

For example cos2x is what, sin2x is what?

Answer 4

Okay try that!

Answer 5

tried...still im not getting it...

Answer 6

show me what did you get!

Answer 7

cosx + sinx = (cosx - sinx) * ( cosx + sinx) + 2sinxcosx

Answer 8

correct up to this ?

Answer 9

Yes! what else did you do?

Answer 10

simplify those parenthesis, you could find new leads!

Answer 11

cosx + sinx = cos2x + sin2x
sin2x - sinx = cos2x - cosx
2cos(3x/2)sin(x/2) = 2sin(3x/2)sin(-x/2)
cos(3x/2)= -sin(3x/2)
tan(3x/2)=-1

Answer 12

oh i forgot something,

tan(3x/2) = tan(3pi/4)
therefor , 3x/2 = n(pi) + 3(pi)/4
x =2(pi)(n+ 3/4)/3

Answer 13

from here cosx + sinx = cos2x + sin2x
to here sin2x - sinx = cos2x - cosx
a sign check the work again

Answer 14

And please explain your steps!

Answer 15

thankyou so much lochana...

Answer 16

my steps were a little complicated i guess...i used the formula of cos2x and sin2x directly cos2x = cos^2x - sin^2x and sin2x = 2cosx*sinx

Answer 17

and thankyou xapproachesinfinity for giving me some sense

Answer 18

Anytime! there are many ways to solving trig equations!
you just need to see what works with what!

Answer 19

@lochana please next time explain your steps!

Answer 20

yeah, thats where the trouble comes in. i dont know when to use which formula...so it all just jumbles up into a mess leaving it more complicated than it is...
but thanks anyways :)

Answer 21

It's okay, we all share that! we all struggle in the beginning, doing this continuously will help you recognize your mistakes and direct you to find or solving problems a lot easier it is a habit by training your mind to this thin

Answer 22

And what I got tan(3x/2)=1 not negative one

Answer 23

I was pushing you to do it and see where you struggle and how you would think it over haha
but lochana intervened lol

Answer 24

@xapproachesinfinity yes you are correct, tan(3x/2)=1,

Answer 25

Alright! thanks!