Find the smallest positive values of `xa n dy` satisfying `x-y=pi/4a n dcotx+coty=2`

Let log_(a)N=alpha + beta where alpha is integer and beta =[0,1) . Then , On the basis of above information , answer the following questions. The difference of largest and smallest integral value of N satisfying alpha =3 and a =5 , is

Find (dy)/(dx) if x-y= pi

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 .

The positive integer value of n >3 satisfying the equation 1/(sin(pi/n))=1/(sin((2pi)/n))+1/(sin((3pi)/n))i s

If x and y are positive acute angles such that (x+y) and (x-y) satisfy the equation tan^(2) theta - 4 tan theta +1=0 , then

Find the value of n such that, ""^(n)P_(2)=30

Let f be a function satisfying of xdot Then f(x y)=(f(x))/y for all positive real numbers xa n dydot If f(30)=20 , then find the value of f(40)dot

The number of values of y in [-2pi,2pi] satisfying the equation abs(sin2x)+abs(cos2x)=abs(siny) is

Statement I Common value(s) of 'x' satisfying the equation . log_(sinx )( sec x +8) gt o and log_(sinx) cos x + log_(cos x ) sin x =2 in (0, 4pi) does not exist. Statement II On solving above trigonometric equations we have to take intersection of trigonometric chains given by sec x gt 1 and x = n pi +(pi)/(4), n in I