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" 8.सिद्ध कीजिए कि "int(0)^( pi/2)(dx)/(...

" 8.सिद्ध कीजिए कि "int_(0)^( pi/2)(dx)/(1+cot x)=(pi)/(4)" ."

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int_(0)^(pi//2)(dx)/((1+cotx))=(pi)/(4)

int_(0)^(pi//2)(dx)/((1+cot^(3)x))=(pi)/(4)

int_(0)^(pi/2)(1)/(1+cot^(4)x)dx=

int_(0)^(pi//2)(dx)/((1+sqrt(tanx)))=(pi)/(4)

Prove that : int_(0)^(pi//2) (dx)/(1+cot x)=(pi)/(4)

int_(0)^( pi/2)(1)/(1+cot^(2)x)dx=?

int_(0)^((pi)/(2)) (1)/(1 + cot x)dx

int_(0)^(pi//2)x cot x dx=(pi)/(2)(log2)

int_(0)^(pi//4) (1)/(1+cos 2x)dx