Question

Identities question below

Answer 1

\[\sin ^{2}x=3\cos ^{2}x\]

Answer 2

I think it is not an identity question.
You are trying to solve for x.

Answer 3

my answer was \[sinx=\frac{ \sqrt{3} }{ 2 } or sinx=-\frac{ \sqrt{3} }{ 2 }\]

Answer 4

@mathmate i am solving for x :) sorry, my main concern is that it doesn't match in the calculator. am i doing something wrong?

Answer 5

\(\bf sin ^2(x)=3cos ^2(x) \implies \cfrac{sin ^2(x)}{cos ^2(x)} =3 \implies tan^2(x) =3\\
tan^{-1}(tan^2(x)) =tan^{-1}(3)\)

Answer 6

hmmm that want whack... one sec :(

Answer 7

\(\bf sin ^2(x)=3cos ^2(x) \implies \cfrac{sin ^2(x)}{cos ^2(x)} =3 \implies tan^2(x) =3\\
tan(x) =\sqrt{3} \implies tan^{-1}(tan(x)) =tan^{-1}(\sqrt{3})\)

Answer 8

\(\bf x = tan^{-1}(\sqrt{3})\)

Answer 9

Try it this way:
\( sin^2x=3cos^2x \)
Divide both sides by \( cos^2x \)
\( \frac{sin^2x}{cos^2x} =3\)
or
\( tan^2x =3\)
\( tan x = \sqrt{3} \)
Between 0 and 360,
x=pi/3 or 4pi/3

Answer 10

Thank you!!

Answer 11

yw!