If `f(x)=sqrt(1-sin2x)` , then `f^(prime)(x)` is equal to `(a) -(cosx+sinx),forx in (pi/4,pi/2)` `(b) cosx+sinx ,forx in (0,pi/4)` `(c) -(cosx+sinx),forx in (0,pi/4)` `(d) cosx-sinx ,forx in (pi/4,pi/2)`

If f(x)=|x|^(|sinx|), then find f^(prime)(-pi/4)

tan^(-1)[(cosx)/(1+sinx)] is equal to pi/4-x/2,forx in (-pi/2,(3pi)/2) pi/4-x/2,forx in (-pi/2,pi/2) pi/4-x/2,forx in (-pi/2,pi/2) pi/4-x/2,forx in (-(3pi)/2,pi/2)

Solve (x-1)|x+1|cosx>0,forx in [-pi,pi]

Which of the following is/are correct ? (a) (tanx)^(ln (cosx))lt(cotx)^(ln(cosx))AAx in(pi/4,pi/2) (b) (sinx)^(ln (secx))gt(cosx)^(ln(cosx))AA x in(0,pi/4) (c ) (sec. pi/3)^(ln (tanx))gt(sec. pi/3)^(ln(cosx))AA x in (pi/4,pi/2) (d) (1/2)^(ln(sinx))gt(3/4)^(ln(sinx))AA x in(0,pi/2)

if f(x)= sinx + cosx for 0 < x < pi/2

Discuss the extremum of f(x)=sinx(1+cosx),x in (0,pi/2)

If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

Solve (sqrt(5)-1)/(sinx)+(sqrt(10+2sqrt(5)))/(cosx)=8,x in (0,pi/2)

If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a) 11-(7pi)/2 (b) (7pi)/2-11 (c) (5pi)/2-11 (d) none of these

int _0^(pi/2) (sin^2x)/(sinx+cosx)dx