Question

solve it. no span. ​

Answer 1

hey !!

let

theta =x

given here

√3 tan x =3 sin x

find here

sin²x-cos²x=?

_________________

Solution :-

√3 tan x =3 sin x

=>√3/3= sin x /tan x

=>√3/3= cos x

=>cos x = 1/√3

_________________

now,

1/cos x= sec x

sec x =√3

_________________________

sin x= √[1- cos²x]

= √[1- (1/√3)²]

=√[1-1/3)

√(3-1)/3

=√(2/3)

__________________________

so,

sin²x - cos ² x

= (√(2/3)² - (1/√3)²

= 2/3 -1/3

= 1/3

__________ ________

I hopes its helps u

follow me...!!

@Abhi.❤❤

Answer 2

hey mate here is your solution
$hence \: \sqrt{3} \tan(theta) = 3 \sin(theta)$
so
$\frac{ \tan(theta) }{sin \: theta} = \frac{3}{ \sqrt{3} } = \frac{ \sqrt{3} \times { \sqrt{3} } }{ \sqrt{3} } = \sqrt{3}$
$\frac{ \frac{\sin(theta) \: }{ \cos(theta) } }{ \sin(theta) } = \frac{ \sin( theta) }{ \cos(theta) } \times \frac{1}{ \sin(theta) } = \frac{1}{ \cos(theta) }$
cos theta =
$\frac{1}{\sqrt{3} }$
so cos square theta = 1/3
therefore sin square theta = 1-cos2 theta
= 1- 1/3= (3-1)/2
=2/3
so
sin 2 theta - cos 2 theta = 2/3 - 1/3
= 1/3 ans.





for more information email ([email protected])