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प्रश्न
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
उत्तर
`32sqrt(3)[sin pi/48 xx cos pi/48] = 16sqrt(3)[2sin pi/48 cos pi/48]`
= `16sqrt(3) sin pi/24((2pi)/48 = pi/24)`
Now `16sqrt(3)[sin pi/24 xx cos pi/24]`
= `8sqrt(3)[2 sin pi/24 cos pi/24]`
= `8sqrt(3)[sin (2pi)/24]`
= `8sqrt(3) sin pi/12`
Now `8sqrt(3)[sin pi/12 cos pi/12]`
= `4sqrt(3)[2 sin pi/12 cos pi/12]`
= `4sqrt(3)[sin (2pi)/12]`
= `4sqrt(3)(sin pi/6)`
Now `4sqrt(3) sin pi/6 cos pi/6 = 2sqrt(3)[2sin pi/6 cos pi/6]`
`2sqrt(3)[sin (2pi)/6] = 2sqrt(3) sin pi/3`
= `2sqrt(3) xx sqrt(3)/2`
= 3
= R.H.S
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