prove that

sin^2 24 - sin^2 6= (5^1/2 - 1 )/8

sin²24 - sin²6 = (5^1/2-1)/8

we have to prove this

sin²A - sin²B = sin(A-B)sin(A+B)

taking LHS

sin²24 - sin²6= sin18sin30=(sin18)/2

sin18 = (5^1/2-1)/4

so LHS becomes

          = (5^1/2-1)/8 =RHS

hence proved

Dear student,

We know that

sin(A + B)sin(A - B) = sin^(2)A - sin^2(2)B

A=24

B=6

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

Dear Student,
Please find below the solution to your problem.

sin224 - sin26 = (51/2-1)/8
we have to prove this
sin2A - sin2B = sin(A-B)sin(A+B)
taking LHS
sin224 - sin26= sin18sin30=(sin18)/2
sin18 = (51/2-1)/4
so LHS becomes
= (51/2-1)/8 =RHS
hence proved

Thanks and Regards