Prove : (tan A)/((1 + tan^2 A) ^ 2) + (cos A)/((1 + cot^2 A) ^ 2) = sin Delta * cos 2
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Answer:
LHS=
(1+tan
2
A)
2
tanA
+
(1+cot
2
A)
2
cotA
(sec
2
A)
2
tanA
+
(cosec
2
A)
2
cotA
=
cos
4
A
1
cosA
sinA
+
sin
4
A
1
sinA
cosA
=sinAcos
3
A+cosAsin
3
A
=sinAcosA[sin
2
A+cos
2
A]
=sinAcosA=RHS
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