1.

Prove that:Sin-1 (1/√17) + cos-1 (9/√85) = tan-1 (1/2)

Answer»

sin-1(\(\frac1{(\sqrt{17})}\)) + cos-1\((\frac9{\sqrt{85}})\)

 = tan-1(\(\frac1{\sqrt{17-1}}\)) + tan-1(\(\frac{\sqrt{85-91}}9\))

 = tan-1(\(\frac14\)) + tan-1(\(\frac29\))

 = tan-1\(\left(\cfrac{\frac14+\frac29}{1-\frac14\times\frac29}\right)\)

 = tan-1\((\frac{9+8}{36-2})\)

= tan-1\((\frac{17}{34})\) = tan-1(\(\frac12\))



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