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Algebra of Functions

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If tan^-1y=5tan^-1, x express as an algebraic function of x and hence show that tan 18^0 is a root of the equation 5u^4 -10u^2 +1=0

Convert the trigonometric function sin[2cos^-1{cot(2tan^-1 x)}] into an algebraic function f(x). Then from thealgebraic functionfind all the values of x for which f(x) is zero. Express the values of x in the form a+-sqrt(b) where a and b are rational numbers.

If tan ^(-1)y=4tan^(-1)x(|x|