If `x+y=pi/4a n dtanx+tany=1,t h e n(n in Z)` (a)`sinx=0a l w a y s` (b)when `x=npi+pi/4t h e ny=-npi` (c)when `x=npit h e ny=npi+(pi/4)` (d)when `x=npi+pi/4t h e ny=npi-(pi/4)`

If sin^3theta+sinthetacos^2theta=1,t h e ntheta is equal to (n in Z) (a) 2npi (b) 2npi+pi/2 (c) 2npi-pi/2 (d) npi

For n in Z , the general solution of (sqrt(3)-1)sintheta+(sqrt(3)+1)costheta=2i s(n in Z) theta=2npi+-pi/4+pi/(12) theta=npi+(-1)^npi/4+pi/(12) theta=2npi+-pi/4 theta=npi+(-1)^npi/4-pi/(12)

A general solution of tan^2theta+cos2theta=1 is (n in Z) npi=pi/4 (b) 2npi+pi/4 npi+pi/4 (d) npi

Ifx^2+y^2=1a n dP=(3x-4x^3)^2+(3y-4y^3)^2,t h e nPi se q u a lto

The n t h derivative of x e^x vanishes when (a) x=0 (b) x=-1 (c) x=-n (d) x=n

The solution of 4sin^2x+tan^2x+cos e c^2x+cot^2x-6=0i s(n in Z) npi+-pi/4 (b) 2npi+-pi/4 npi+pi/3 (d) npi-pi/6

If 4sin^4x+cos^4x=1 ,then x is equal to (n in Z) (a) npi (b) npi+-sin^(-1)sqrt(2/5) (c) (2npi)/3 (d) 2npi+-pi/4

If sintheta=1/2a n dcostheta=-(sqrt(3))/2, then the general value of theta is (n in Z)dot (a) 2npi+(5pi)/6 (b) 2npi+pi/6 2npi+(7pi)/6 (d) 2npi+pi/4

If y=f(a^x)a n df^(prime)(sinx)=(log)_e x ,t h e nfin d(dy)/(dx), if it exists, where pi/2

x y=(x+y)6na n d(dy)/(dx)=y/x t h e nn= 1 b. 2 c. 3 d. 4