sin²alpha× tan alpha+ cos²alpha× cot alpha+ 2 sin alpha cos alpha=
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LHS=(sinα+cosα)(tanα+cotα)
=(sinα+cosα)(
cosα
sinα
+
sinα
cosα
)
=sinα+cosα(
cosαsinα
sin
2
α+cos
2
α
)
=
sinαcosα
sinα+cosα
=
cosα
1
+
sinα
1
=secα+cscα
=RHS
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