Prove that `sec^(2) (tan ^(-1) 3) + cosec^(2)(cot^(-1)2) = 15`

1.	Prove that `sec^(2) (tan ^(-1) 3) + cosec^(2)(cot^(-1)2) = 15`
Answer» Let `tan^(-1) 3 = A and cot^(-1) 2 = B` `rArr" " tanA = 3 and cot B = 2 ` `L.H.S = sec^(2) (tan ^(-1)3)+ cosec^(2) (cot^(-1)2)` `= sec^(2) A + cosec^(2) (cot^(-1) 2)` `= sec^(2)A + cosec^(2) B` `= 1 + tan^(2)A + 1 + cot ^(2)B` `2+3 ^(2)+2^(2) = 15 = R.H.S`

Discussion

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