For the equation `1-2x-x^2=tan^2(x+y)+cot^2(x+y)` (a)exactly one value of `x` exists (b)exactly two values of `x` exists (c)`y=-1+npi+pi/4,n in Z` (d)`y=1+npi+pi/4, n in Z`

Equation 1+x^2+2x"sin"(cos^(-1)y)=0 is satisfied by (a) exactly one value of x (b) exactly two value of x (c) exactly one value of y (d) exactly two value of y

Let tanx-tan^2x >0 and |2sinx| (a) x > npi,n in Z (b) x > npi-pi/6,n in Z (c) x (d) x < npi+pi/6, n in Z

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

If tan^-1(1/y)=-pi+cot^-1 y, where y=x^2-3x+2, then find the value of x

If 2tan^2x-5secx=1 for exactly seven distinct value of x in [0,(npi)/2],n in N then find the greatest value of ndot

Consider the system of linear equations in x , ya n dz : ""(sin3theta)x-y+z=0 , (cos2theta)x+4y+3z=0 , 2x+7y+7z=0 Which of the following can be the value of theta for which the system has a non-trivial solution (A) npi+(-1)^npi/6,AAn in Z (B) npi+(-1)^npi/3,AAn in Z (C) npi+(-1)^npi/9,AAn in Z (D)none of these

Statement-I: General solution of the equation (tan4x - tan2x)/(1+tan4x tan2x) =1 is x = (npi)/2 + pi/8, n int Z Statement-II: tanalpha=1 , therefore general solution is alpha= npi + pi/4, n int Z

There are two circles whose equation are x^2+y^2=9 and x^2+y^2-8x-6y+n^2=0,n in Zdot If the two circles have exactly two common tangents, then the number of possible values of n is (a)2 (b) 8 (c) 9 (d) none of these

The set of values of x satisfying the equation sin3alpha=4sinalphasin(x+alpha)sin(x-alpha) is (a) npi+-pi/4,AAn in Z (b) npi+-pi/3,AAn in Z (c) npi+-pi/9,AAn in Z (d) npi+-pi/(12),AAn in Z