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cos^-1(4/5)+sin^-1(5/13) =tan^-1(56/33)...

`cos^-1(4/5)+sin^-1(5/13) =tan^-1(56/33)`

Text Solution

Verified by Experts

`cos^-1 4/5 = theta`
`cos theta = 4/5`
`sin theta = 3/5`
`theta = sin^-1 ( 3/5)`
`sin^-1 (3/5) + sin^-1(5/13)`
`sin^-1 x + sin^-1 y = sin^-1 ( x sqrt(1-y^2) + ysqrt(1 - x^2))`
`sin^-1 ( 3/5sqrt(1 - (5/13)^2 ) + 5/3 sqrt(1 - (3/5)^2 ) )`
`sin^-1(3/5 sqrt(144/169) + 5/13sqrt(16/25))`
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Show that cos^-1(4/5)+cos^-1(12/13)=tan^-1(56/33)

Prove that : sin^-1 (3/5) + sin^-1 (5/13) = cos^-1 (33/65)

Prove that sin^-1(4/5) + cos^-1 (12/13) = tan^-1 (63/16)

Prove that : cos^-1 (4/5) + cos^-1(12/13) = cos^-1 (33/65)

Prove that : sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)

Prove that: sin^-1 (3/5) +cos^-1 (12/13)+cot^-1 (56/33)=pi/2

Prove that: sin^-1 (3/5) +cos^-1 (12/13)+cot^-1 (56/33)=pi/2

Prove that cos^(-1)(12/13)+sin^(-1)(4/5)=tan^(-1)(63/16) .

Prove that cos^-1(4/5)+cos^-1(12/13)=cos^-1(33/65) .

Prove that : cos(sin^-1(3/5) + sin^-1 (5/13)) = 33/65