Question

sin3x = cos3x for 0<=x<=360

Answer 1

You know the formula for sin3x and cos3x?

Answer 2

nope

Answer 3

3sin(x) – 4(sin(x))^3
4cos^3x - 3cosx..
equate this..

Answer 4

i dont understand :(

Answer 5

oh sorry.
i meant sin3x=3sin(x) – 4(sin(x))^3
cos3x=4cos^3x - 3cosx..

Answer 6

ok can you please solve it for me now?

Answer 7

you just need to equate them and evaluate. Do it and tell me where you are getting stuck. I'll help you.
3sin(x) – 4(sin(x))^3 = 4cos^3x - 3cosx
You just need to solve this..

Answer 8

do we need to find the values of x?

Answer 9

3sin(x) – 4(sin(x))^3 = 4cos^3x - 3cosx
ok so i am up to here. What do i do next?

Answer 10

reaarange them..
3(sinx + cosx) = 4[sin^3(x) + cos^3(x)]
.. to the RHS apply the formula for a^3 + b^3= (a+b)(a^2 - ab + b^2)..

Answer 11

@yrelhan4
what do we need to find in this ques?

Answer 12

value of x, maybe.. @niksva

Answer 13

wait. i'll see.

Answer 14

then buddy can i suggest u a different method if u guys dont mind

Answer 15

yes please

Answer 16

Go ahead..
and 3(sinx + cosx)=4[(six+cosx) (sin^2x - sinxcosx + cons^2x)
3/4(sinx + cosx)=[(six+cosx) (1-sinxcosx)]
3/4=(1-sinxcosx)
sinxcosx= 1-(3/4)
sinxcosx=1/4
sin2x=1/8
that should be it..

Answer 17

can we write cos3x = sin(pi/2 - 3x) ?

Answer 18

first step is
sin3x = cos3x

second step would be
sin3x = sin (pi/2 - 3x)

is that clear?

Answer 19

@yrelhan4 can you now solve sin2x = 1/8?

Answer 20

oh dang. this is way easier than i made it look. sorry about that..
divide by cos3x on the both sides..
tan3x=1
3x=arctan1
3x=45
x=15..
sigh.

Answer 21

and @niksva method is right too. follow any of these.
but ignore what i did earlier.

Answer 22

first method is used in those problems where u have to simplify the expressions
hope this will help

Answer 23

thanks guys :)