[tex]sin^{2}1 + sin^{2}2 +sin^{2} 3+.............. +sin^{2}89 = ?
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Answer:
ANSWER
1+sin2A−cos2A
1+sin2A+cos2A
=
sin2A+1−(1−2sin
2
A)
sin2A+1+2cos
2
A−1
=
2sinAcosA+2sin
2
A
2sinAcosA+2cos
2
A
=
2sinA(cosA+sinA)
2cosA(sinA+cosA)
=
sinA
cosA
=cotA.
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