If ` tan x = ( 5)/( 12), ` then find sec x.

If the sum of all value of x satisfying the system of equations tan x + tan y+ tan x* tan y=5 sin (x +y)=4 cos x * cos y is (k pi )/2 , where x in (0, (pi)/(2)) then find the values of k .

If y = tan x tan 2x tan 3x, (sin 12x != 0) then dy / dx has the value equal to

If y= x^(tan x) + sqrt((x^(2) + 1)/(x)) then find (dy)/(dx)

If sec x cos 5x=-1 and 0 lt x lt (pi)/(4) , then x is equal to

If (tan^(-1) x)^2 + (cot^(-1) x)^2 = (5 pi^2) /8 find x.

Find the values of each of the following : tan^(-1)2x+tan^(-1)(1/(x+4))=pi/2 then find x.

If "tan"^(-1)(x-1)/(x-2)+"tan"^(-1)(x+1)/(x+2)=pi/4 , then find the value of x

y= sin^(-1) [(5x + 12 sqrt(1-x^(2)))/(13)] then find (dy)/(dx)

u= f (tan x), v= g(sec x), f'(1) =2 and g'(sqrt2)= 4 " then " (du)/(dv)|_(x = (pi)/(4)) =……….