If `0ltxltpi/2` then `sinx/x` is

If 0ltxltpi and cosx+sinx=1/2 then tanx=

If f(x)=int_0^sinx cos^-1t dt+int_0^cosx sin^-1t dt, 0ltxltpi/2 , then f(pi/4)= (A) 0 (B) pi/sqrt(2) (C) 1 (D) pi/(2sqrt(2))

If f(x)=int_0^sinx cos^-1t dt+int_0^cosx sin^-1t dt, 0ltxltpi/2 , then f(pi/4)= (A) 0 (B) pi/sqrt(2) (C) 1 (D) none of these

If 0ltxltpi and cosx + sinx = 1//2 , then tanx is :

If 0ltxltpi/4andcosx+sinx=5/4 , then the value of 16(cosx-sinx)^2 is ___________ .

If 0ltxltpi/4andcosx+sinx=3/5 , then the value of 25(cosx-sinx)^2 is ___________ .

If 0ltxltpi/4andcosx+sinx=5/4 , then the value of 16(cosx-sinx)^2 is ___________ .

Let 0ltxltpi//4 , then (sec2x-tan2x) equals

If 0ltxltpi and cosx + sinx =1/2 , then tanx is (1) (4-sqrt(7))/3 (2) -(4+sqrt(7))/3 ( 3) (1+sqrt(7))/4 (4) (1-sqrt(7))/4

If f''(x)gt0 and f'(1)=0 such that g(x)=f(cot^2x+2cotx+2) , where 0ltxltpi then the interval in which g(x) is decreasing is :