Question

(square root of 3)sine(theta) + cosine(theta) = 1

Answer 1

\(\Huge\color{blue}{ \sf \sqrt{3} \times sin(x)+cos(x)=1 }\)


LIKE THIS ?

Answer 2

yes

Answer 3

\(\Huge\color{blue}{ \sf \sqrt{3} \times \sqrt{sin^2(x)} ~+~\sqrt{1-sin^2(x)}=0 }\)


\(\Huge\color{blue}{ \sf \sqrt{3sin^2(x)} ~+~\sqrt{1-sin^2(x)}=0 }\)


\(\Huge\color{blue}{ \sf \sqrt{3sin^2(x)} =-\sqrt{1-sin^2(x)} }\)


\(\Huge\color{blue}{ \sf 3sin^2(x)=-(~~1-sin^2(x) ~~)}\)

Answer 4

can you solve it now?

Answer 5

oh yes, i got it now, thanks

Answer 6

oh, no minus on the right side

Answer 7

\(\Huge\color{blue}{ \sf \sqrt{3sin^2(x)} =\sqrt{1-sin^2(x)} }\)

Answer 8

(b/c I squared both sides and (-3)^2= POSITIVE 9 )

Answer 9

and no roots, sorry. If you don't get what I meant tell me.

Answer 10

im a little lost, where does the positive 9 come from?

Answer 11

\(\Huge\color{olive}{ \it 3Sin^2(x)=1-Sin^2(x) }\)

Answer 12

okay i think i can take it from here

Answer 13

Tell me what you get as your final answer, to make sure you solve it correctly.

I would prefer you to post the steps here (you can ask for any latex needed, and use equation editor, or just draw it using a drawing tool below )
but if you don't want to post your work here, it's totally fine ;)

Answer 14

okay will do

Answer 15

\[3\sin ^{2}(x)-1+\sin ^{2}(x)=0\]

Answer 16

\[4\sin ^{2}(x)-1=0\]

Answer 17

yeah. THEN....


add 1 to both sides
divide both sides by 4
square-root both sides
and take "inverse-sine" of what you get on the right side.