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