English, asked by Riya1045, 1 month ago

Accha toh janaab humse gussa ho gye hain

if sin^2 + 3 cos^2=4 then show that tanO°=1/√3​

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Answers

Answered by riyaa22131
1

4sin 2 θ+3(sin 2 θ+cos 2 θ)=44sin 2 θ+3=44sin 2 θ=1⇒sinθ= 21AC 2 =AB 2 +BC 24−1=AB⇒AB= 3tanθ= BABC = 31

Answered by Aaradhyamishra2012
1

We have:

sin

2

(

θ

)

+

3

cos

2

(

θ

)

=

4

which really is just:

sin

2

(

θ

)

+

cos

2

(

θ

)

+

2

cos

2

(

θ

)

=

4

and using the identity

sin

2

(

x

)

+

cos

2

(

x

)

=

1

for all

x

, we get:

1

+

2

cos

2

(

θ

)

=

4

(eq.A)

We carry on and simplify eq.A until we get an expression for

cos

(

θ

)

:

2

cos

2

(

θ

)

=

3

cos

2

(

θ

)

=

3

2

cos

(

θ

)

=

±

3

2

We also notice that

cos

2

(

θ

)

=

1

sin

2

(

θ

)

, so (eq.A) becomes:

1

+

2

cos

2

(

θ

)

=

1

+

2

(

1

sin

2

(

θ

)

)

=

4

i.e.

3

2

sin

2

(

θ

)

=

4

i.e.

sin

2

(

θ

)

=

1

2

sin

(

θ

)

=

±

1

2

(it should really be 'minus-plus' instead but the symbol does not exist here in Socratic).

So, now it is simply a matter of plugging these in the

tan

function:

tan

(

θ

)

=

sin

(

θ

)

cos

(

θ

)

=

±

1

2

±√32=±(1√3)=±√33

(it is more conventional to write it like this without the square-root in the denominator).

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