Question

Sin-1 8/17 +sin-1 3/5 = tan-1 77/36

Answer 1

Answer:

Step-by-step explanation:

माना  L.H.S.  =  Θ,  तब   Θ >0

और    $\theta=\sin^{-1}(\dfrac{8}{17} )+\sin^{-1}(\dfrac{3}{17} )\\\\\\<\sin^{-1}\dfrac{1}{\sqrt{2} } +\sin^{-1}\dfrac{1}{\sqrt{2} }=\dfrac{\pi}{4} +\dfrac{\pi}{4} =\dfrac{\pi}{2}$

sin^{-1}x [-1,1] बढ़ता है और  3/5, 8/17 < 1/√2 )

तथा  

       $\sin\theta=\sin(sin^{-1}(\dfrac{8}{17} )+sin^{-1}(\dfrac{3}{5} ))\\\\\\=sin(sin^{-1}(\dfrac{8}{17} )) cos(sin^{-1}(\dfrac{3}{5} ))+cos(sin^{-1}(\dfrac{8}{17} ))sin(sin^{-1}(\dfrac{3}{5} ))\\\\\\=(\dfrac{8}{17} )\sqrt{1-(3/5)^2} +\sqrt{1-(8/17)^2} (3/5)\\\\\\=\dfrac{8}{17} *\dfrac{4}{5}+\dfrac{15}{17}*\dfrac{3}{5}\\\\\\=\dfrac{77}{85}\\\\=> \theta=sin^{-1}(\dfrac{77}{85})\\\\\\\\sin^{-1}(\dfrac{8}{17})+sin^{-1}(\dfrac{3}{5})=sin^{-1}(\dfrac{77}{85})$