If the line `xcostheta+ysintheta=P` is the normal to the curve `(x+a)y=1,` then show `theta in (2npi+pi/2,(2n+1)pi)uu(2npi+(3pi)/2,(2n+2)pi),n in Z`

The expression cos3 theta+sin3 theta+(2sin2 theta-3)(sin theta-cos theta) is positive for all theta in (2n pi-(3 pi)/(4),2n pi+(pi)/(4)),n in Z(2n pi-(pi)/(4),2n pi+(pi)/(6)),n in Z(2n pi-(pi)/(3),2n pi+(3 pi)/(3)),n in Z(2n pi-(pi)/(4),2n pi+(3 pi)/(4)),n in Z

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

The straight line x cos theta+y sin theta=2 will touch the circle x^(2)+y^(2)-2x=0 if theta=n pi,n in IQ(b)A=(2n+1)pi,n in Itheta=2n pi,n in I(d) none of these

The period of f(x)=sin((pi x)/(n-1))+cos((pi x)/(n)),n in Z,n>2

If cot theta-tan theta=sec theta, then theta is equal to 2n pi+(3 pi)/(2),nZ b.n pi+(-1)^(n)(pi)/(6),nZ c.n pi+(pi)/(2),nZ d.none of these

The value(s) of theta , which satisfy 3-2\ costheta-4sintheta-cos2theta+sin2theta=0 is/are theta=2npi; n in I (b) 2npi+pi/2; n in I 2npi-pi/2; n in I (d) npi: n in I

The value(s) of theta, which satisfy the equation : 2cos^3 3thetatheta+4=3sin^2 3theta is/are (2npi)/3+(2pi)/9,\ n in I (b) (2npi)/3-(2pi)/9,\ n in I\ (2npi)/5+(2pi)/5,\ n in I\ (d) (2npi)/5-(2pi)/5,\ n in I

If A=[cos theta-sin theta sin theta cos theta], then A^(T)+A=I_(2), if theta=n pi,n in Z(b)theta=(2n+1)(pi)/(2),quad n in Z(c)theta=2n pi+(pi)/(3),quad n in Z(d) none of these

If (1)/(6)sin theta,cos theta and tan theta are in GP,then the general value of theta is (i) 2n pi+-(pi)/(3)( ii) 2n pi+-(pi)/(6) (iii) 2n pi+-(-1)^(n)(pi)/(3)( iv )n pi+-(pi)/(3)

If cos ecx=1+cot x then x=2n pi,2n pi+(pi)/(2)