one term of an arithmetic sequence is 36 and its common difference is 6.can the sum of any 20 terms be 2751?
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cosθ=cosαcosβ
∴cosβ=
cosα
cosθ
......(1)
R.H.S=tan
2
2
β
=
sin
2
β
(1−cosβ)
2
⇒
1−cos
2
β
(1−cosβ)
2
=
(1−cosβ)(1+cosβ)
(1−cosβ)
2
⇒
(1+cosβ)
(1−cosβ)
=
1+
cosα
cosθ
1−
cosα
cosθ
=
cosα+cosθ
cosα−cosθ
=
2cos(
2
α+θ
)sin(
2
θ−α
)
2sin(
2
α+θ
)sin(
2
α−θ
)
=tan(
2
θ+α
)tan(
2
θ−α
)
=L.H.S
Hence proved.
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