1.

Prove that - sec2 (tan-1 2) + cosec2 (cot-1 3) = 15

Answer»

L.H.S. = sec2(tan-1 2) + cosec2(cot-1 3)

Let tan-1 2 = α

tan α = 2

∵ sec2 α = 1 + tan2 α

1 + 22 = 1 + 4 = 5

sec2 α = 5

Let again cot-1 3 = β

cot β = 3

∴ sec2 α + cosec2 β

5 + 1 + cotβ

= 5 + 1 + (3)2

= 5 + 1 + 9 = 15 = R.H.S.



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