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If x=5+2√6 and tany=1/2(√x+1/√x) then find the value of sec^2y+sin^2y.

If x=5+2√6 and tany=1/2(√x+1/√x) then find the value of sec^2y+sin^2y.

Grade:12th pass

1 Answers

Lab Bhattacharjee
121 Points
5 years ago
x=5+2\sqrt6=(\sqrt3+\sqrt2)^2 \implies \sqrt x=\sqrt3+\sqrt2, \dfrac1{\sqrt x}=\cdots=\sqrt3-\sqrt2 \\ \text{ Now use } \sin^2y=\dfrac1{1+\cot^2y}=\dfrac{\tan^2y}{\tan^2y+1} \\ \text{and } \sec^2y=\tan^2y+1

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