Question

sin^2 24° - sin^26° = (√5 - 1)/8​

Answer 1

Answer:

√5-1

-------------

8

Step-by-step explanation:

I think there is a mistake in question

question is like this

√5-1

sin²24*-sin²6*=------------

8

now

L. H. S. =sin²24*-sin²6*

we have a identity

sin²A-sin²B=sin(A+B) sin(A-B)

applying this

=sin(24*+6*) sin (24*-6*)

=sin 30* sin 18*

we know that

1 √5-1

sin 30*=----- and sin18*= ----------

2 4

putting these values

1 √5-1

=--------- ---------------

2 4

√5-1

=---------------=RHS

8

additional information----->

______________________

√(10+2√5)

cos18*=-----------------

4

√5-1

sin72* = -------------

4

√5+1

cos36*=-------------

4

√10-2√5

sin 36*= --------------

4

Hope it helps you

have a nice day

Answer 2

To prove -

sin²24° - sin²6° = (√5-1)/8

Solution -

LHS

As we know that

sin²a - sin²b = sin(a+b)sin(a-b)

Then , sin(24+6)sin(24-6)

→sin 30° .sin18°

→ sin 30 = 1/2 and

$= > \sin(18) = \frac{ \sqrt{5} - 1}{4}$

$= > \frac{1}{2} \times \frac{ \sqrt{5} - 1 }{4}$

$= > \frac{ \sqrt{5} - 1 }{8}$

LHS= RHS

hence proved

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