If sin 2x+cosx=0 , then which among the following is /are true ?
I. cosx =0 , II. `sinx=-(1)/(2)` , III `x=(2n+1)(pi)/(2),ninZ` , IV. `x=npi+(-1)^(n)(7pi)/(6),ninZ`

If cosecx=1+cotx, then x=2npi,2npi+(pi)/(2),ninZ .

Let f(x)=((2sinx+sin2x)/(2cosx+sin2x)*(1-cosx)/(1-sinx)): x in R. Consider the following statements. I. Domain of f is R. II. Range of f is R. III. Domain of f is R-(4n-1)pi/2, n in I. IV. Domain of f is R-(4n+1)pi/2, n in I. Which of the following is correct?

Let f(x)=((2sinx+sin2x)/(2cosx+sin2x)*(1-cosx)/(1-sinx)): x in R. Consider the following statements. I. Domain of f is R. II. Range of f is R. III. Domain of f is R-(4n-1)pi/2, n in I. IV. Domain of f is R-(4n+1)pi/2, n in I. Which of the following is correct?

Let f(x)=((2sinx+sin2x)/(2cosx+sin2x)*(1-cosx)/(1-sinx)): x in R. Consider the following statements. I. Domain of f is R. II. Range of f is R. III. Domain of f is R-(4n-1)pi/2, n in I. IV. Domain of f is R-(4n+1)pi/2, n in I. Which of the following is correct?

Let f(x)=((2sinx+sin2x)/(2cosx+sin2x)*(1-cosx)/(1-sinx)): x in R. Consider the following statements. I. Domain of f is R. II. Range of f is R. III. Domain of f is R-(4n-1)pi/2, n in I. IV. Domain of f is R-(4n+1)pi/2, n in I. Which of the following is correct?

The general solution of the following equation : 2(sinx-cos2x)-sin2x)\ (1+2sinx)+2cosx=0 is/are x=2npi\ ;\ n in I (b) npi+(-1)^n(-pi/2);\ n in I x=npi+(-1)^npi/6;\ n in I x=npi+(-1)^npi/4;\ n in I

sin^(2) x+2sin x cos x-3cos^(2) x = 0 if (i) tan x = 3 (ii) tan x = -1 (iii) x = n pi+(pi)/(4) , n in I (iv) x = n pi+tan^(-1) (3), n in I

If I_n=int_(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... then which one of the following is not true ?

If I_n=int_(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... then which one of the following is not true ?