Home
Class 12
MATHS
Prove that:sin^(-1)8/(17)+sin^(-1)3/5=ta...

Prove that:`sin^(-1)8/(17)+sin^(-1)3/5=tan^(-1)(77)/(36)`

Text Solution

Verified by Experts

LHS=`sin^(-1)""(8)/(17)+sin^(-1)""(3)/(5)`
`=sin^(-1)""[(8)/(17)sqrt(1-((3)/(4))^(2))+(3)/(5)sqrt(1-((8)/(17))^(2))]`
`=sin^(-1)[(8)/(17)xx(4)/(5)+(3)/(5)xx(15)/(17)]`
`( :.sin^(1)x=tan^(-1)""(x)/(sqrt(1-x^(2))))`
`=sin^(-1)""(77)/(85)=tan^(-1)""(77//85)/(sqrt(1-((77)/(85))^(2)))`
`tan^(-1)((77//875)/(36//85))=tan^(-1)""(77)/(36)`= RHS Hence proved.
Promotional Banner

Topper's Solved these Questions

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise (prove That )|9 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exericse 2.2|21 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|44 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|9 Videos

Similar Questions

Explore conceptually related problems

Prove that : sin^(-1)(8/(17))+sin^(-1)(3/5)=sin^(-1)((77)/(85))=tan^(-1)((77)/(36))

Prove that: sin^(-1)((8)/(17))+sin^(-1)((3)/(5))=tan^(-1)((77)/(6))

Show that : sin^(-1)(8/(17))+sin^(-1)(3/5)=sin^(-1)(77/85)

Prove that sin^(-1) . 8/17 +sin^(-1) . 3/5 = sin^(-1) . 77/85

Prove that sin^(-1) . 8/17 +cos^(-1). 4/5 = cot^(-1) ((36)/77)

Prove that sin^(-1)((8)/(17))+sin^(-1)((3)/(5))=cos^(-1)((36)/(85))

Prove that tan^(-1) (1/8) +tan^(-1) (1/5) =tan^(-1) (1/3)

Prove that : 2 sin^(-1)( 3/5) = tan^(-1)( 24/7)

Prove that sin^(-1) . 8/17 +cos^(-1) . 4/5 = cos^(-1). 36/85

Prove that: ,,2sin^(-1)(3)/(5)=tan^(-1)(24)/(7)