Let `tanx-tan^2x >0` and `|2s inx|<1` . Then the intersection of which of the following two sets satisfies both the inequalities? `x > npi,n in Z` (b) `x > npi-pi/6,n in Z` `x

Which of the following set of values of x satisfies the equation 2^(2sin^2x-3sinx+1)+2^(2-2sin^2x+3sinx)=9? (a) x=npi+-pi/6,n in I (b) x=npi+-pi/3, n in I (c) x=npi,n in I (d) x=2npi+pi/2,n in I

The expression cos3theta+sin3theta+(2sin2theta-3)(sintheta-costheta) is positive for all theta in (a) (2npi-(3pi)/4,2npi+pi/4),n in Z (b) (2npi-pi/4,2npi+pi/6),n in Z (c) (2npi-pi/3,2npi+pi/3),n in Z (d) (2npi-pi/4,2npi+(3pi)/4),n in Z

If the vectors vec aa n d vec b are linearly idependent satisfying (sqrt(3)tantheta+1 )veca+(sqrt(3)s e ctheta-2) vec b=0, then the most general values of theta are a. npi-pi/6, n in Z b. 2npi+-(11pi)/6, n in Z c. npi+-pi/6, n in Z d. 2npi+(11pi)/6, n in Z

The general solution of the equation sin^(100)x-cos^(100)x=1 is 2npi+pi/3,n in I (b) n pi+pi/2,n in I npi+pi/4,n in I (d) 2npi=pi/3,n in I

Which of the following is not the general solution of 2^(cos2x)+1=3. 2^-sin^(2x)? (a) npi,n in Z (b) (n+1/2)pi,n in Z (n-1/2)pi,n in Z (d) none of these

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

General solution of sin^2x-5sinxcosx-6cos^2x=0 is x=npi-pi/4,n in Z only n pi+tan^(-1)6,n in Zon l y both (a) and (b) none of these

The function f(x) is defined on the interval [0.1] Then match the following columns Column I: Function, Column II: Domain f(tanx) , p. [2npi-ddotpi/2,2npi+pi/2],n in Z f(sinx) , q. [2npi,2npi+pi/6]uu[2npi+(5pi)/6,(2n+1)pi],n in Z f(cosx) , r. [2npi,(2n+1)pi],n in Z f(2sinx) , s. [npi,npi+pi/4],n in Z

The solutions of the equation 1+(sinx-cosx)sinpi/4=2cos^2(5x)/2 is/are x=(npi)/3+pi/8, n in Z x=(npi)/2+(5pi)/(16), n in Z x=(npi)/3+pi/4, n in Z x=(npi)/2+(7pi)/8, n in Z

Which of the following is not the solution of the equation sin5x=16sin^5x(n in Z)? npi (b) npi+pi/6 (c) npi-pi/6 (d) none of these