`If (costheta +isintheta)(cos2theta +isin2theta).....(cosntheta + isinntheta) = 1 ` then the value of `theta` is:

If sintheta+costheta=1 , then the value of sin2theta is

costheta+cos2theta+cos3theta+.......+cos(n-1)theta+cosntheta=

If (3+2isintheta)/(1- 2isintheta) is real , then general value of theta is :

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?

Express the following in a + ib form: (i) ((cos theta+ isin theta)/(sin theta + icos theta))^(4) (ii) ((cos 2theta -isin2theta)^(4)(cos4theta +isin4theta)^(-5))/((cos 3theta +isin3theta)^(-2) (cos 3theta -isin 3theta)^(-9)) (iii) ((sinpi//8 +icos pi//8)^(8))/((sinpi//8-icospi//8)^(8))

If costheta+cos3theta+cos5theta+cos7theta=0 , then general value of theta is:

If |{:(1+cos^(2)theta,sin^(2)theta,4cos6theta),(cos^(2)theta,1+sin^(2)theta,4cos6theta),(cos^(2)theta,sin^(2)theta,1+4cos6theta):}|=0 , and theta in (0,(pi)/(3)) , then value of theta is

If cos2theta+9sin2theta-6sintheta+54costheta=1, then the value of 100 tan^2theta +9+14 is equal to

If cos2theta=0 , then |(0,costheta,sin theta),(cos theta, sin theta, 0),(sin theta, 0, cos theta)|^(2) is equal to…………

Let z=(costheta+isintheta)/(costheta-isintheta), pi/4 lt theta lt pi/2 . Then arg(z) =