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Prove that ^{2} (^{-1}2)+ ^{2} (^{-1} 3)=15.

Question

Prove that $sec^{2} (tan^{- 1} 2) + csc^{2} (cot^{- 1} 3) = 15$ .

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Prove that

sec^{2} (tan^{- 1} 2) + csc^{2} (cot^{- 1} 3) = 15

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Text solutionVerified

se c^{2} (t a n^{- 1} 2) + cose c^{2} (co t^{- 1} 3) = 15

LHS :

\Rightarrow se c^{2} (t a n^{1} 2) + cose c^{2} (co t^{- 1} 3)

\Rightarrow {sec (t a n^{1} 2)}^{2} + {cosec (co t^{1} 3)}^{2}

[sec (se c^{- 1} \frac{5}{1})]^{2} + [cosec (cose c^{- 1} 10)]^{2}

= (5)^{2} + (10)^{2}

= 5 + 10

= 15

= RHS

Hence proved

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