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Sec^{2}\left ( tan^{-1}2 \right )+ cosec^{2}\left ( cot^{-1}3 \right )  is equal to

  • Option 1)

    5

  • Option 2)

    13

  • Option 3)

    15

  • Option 4)

    6

 

Answers (1)

best_answer

Sec^{2}\left ( tan^{-1}2 \right )+ cosec^{2}\left ( cot^{-1}3 \right )

\Rightarrow 1+\tan ^{2}\alpha + 1 + \cot ^{2}\beta

\Rightarrow 2+\tan ^{2}\alpha + \cot ^{2}\beta

\Rightarrow 2 + \left ( 2 \right )^{2}+\left ( 3 \right )^{2}

\Rightarrow 2 + 4 + 9 = 15 \ \left [ where\ \tan ^{-1}2 = \alpha \and\ \cot ^{-1}3 = \beta \ \right ]


Option 1)

5

This option is incorrect

Option 2)

13

This option is incorrect

Option 3)

15

This option is correct

Option 4)

6

This option is incorrect

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