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Derivative of One Function w.r.t Another

20.If m and M...

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20.If m and M are such that m <=(tan^-1x)^2+ (cos^-1x)^2<=M then M/m equals.

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Q. The value(s) of

m

such that the roots of the quadratic equation

(m + 1) x^{2} + (m + 1) x - m + 1 = 0

m

, if the quadratic equation

(m - 1) x^{2} - 2 (m - 1) x + 1 = 0

has real equal roots.

Q. The equation

(m + 1) x^{2} + 2 m x + 5 x + m + 3 = 0

has equal roots Find the value of m

α

β

are acute angle such that

tan α = \frac{m}{m + 1}

tan β = \frac{1}{2 m + 1}

. Then find m if

α + β = \frac{π}{m}

(m - 1) x^{2} + m x + 1 = 0

has roots less than

2

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