Question

Sec²(cot⁻¹3) +cosec²(tan⁻¹2)

Answer 1

Answer:

We have to find the value of sec²{tan^-1(2)}+cosec² {cot^-1(3)}

sec²{tan^-1(2)}+cosec² {cot^-1(3)} = [sec{tan^-1(2)}]² + [cosec{cot^-1(3)}]²

Let tan^-1 (2) = A

tanA = 2 => secA = √5 .......(1)

similarly, cot^-1(3) = B

cotB = 3 => cosecB = √10...........(2)

[sec{tan^-1(2)}]² + [cosec{cot^-1(3)}]² = [secA]² + [cosecB]²

from equations (1) and (2),

= √5² + √10²

= 5 + 10 = 15

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