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[" A particle "P" is moving on a circle under the action of only one force acting always towards fixed "],[" point "0" on the circumference.Find ratio of "(d^(2)theta)/(dt^(2))" and "((d theta)/(dt))^(2)" at the moment when "theta=45^(@)" ."],[qquad 0((pi^(F))/(C))]

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int_ (0) ^ (pi / 2) ((theta) / (sin theta)) ^ (2) d theta =

int_(0)^( pi/2)sin^(2)theta d theta=

int_(0)^( pi/2)sin^(2)theta d theta=

int_(0)^(pi//2) (sin^(2)theta)/ (1+cos theta)^(2) d theta =

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int_(0)^((pi)/(4))theta sec^(2)theta d theta