Home
Class 12
MATHS
Prove that sec^(2) (tan ^(-1) 3) + cose...

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

Text Solution

Verified by Experts

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`
Promotional Banner

Topper's Solved these Questions

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exericse 2a|34 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exericse 2b|10 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|44 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|9 Videos

Similar Questions

Explore conceptually related problems

sec^(2) (tan^(-1) 4) + cosec^(2) (cot ^(-1) 3) =?

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

sec^(2) (tan^(-1) 2) + cosec^(2) (cot^(-1) 3) is equal to

Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(sec^(-1)2)+cot^2(cos e c^(-1)3)=11

Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(sec^(-1)2)+cot^2(cos e c^(-1)3)=11

prove that : tan ^(2) (sec ^(-1) 2) + cot ^(2) (cosec ^(-1)3) = 11.

Prove that : 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x

Prove that sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x = x, " where " x in [0,1]

Prove that 1+cot^(2) theta = cosec^(2) theta

Prove that : (sec^(2)A-1)("cosec"^(2)A-1)=1