`(1+cos theta+i sintheta)^n=`

If n is an integer then show that (1 + cos theta + i sin theta)^(n) + (1 + cos theta - i sin theta )^(n) = 2^(n+1) cos ^(n) ( theta//2) cos ((n theta)/2) .

The value of (cos2 theta + i sin 2 theta)^5(sin theta+i cos theta)^4 is

(i) {:[( cos theta , -sin theta ),( sin theta , cos theta ) ]:}" " (ii) {:[( x^(2) -x+1,x-1),( x+1,x+1) ]:}

If theta=pi/6, then the 10th term of the series 1+(costheta+isintheta)+(cos theta+i sin theta)^2+ …. Is

If A = [(cos theta, sin theta),(-sin theta, cos theta)] then show that for all the positive integers n, A^(n) = [(cos n theta,sin n theta),(-sin n theta,cos n theta)] .

If I=[(1,0),(0,1)]=J[(0,1),(-1,0)] and B=[(cos theta, sin theta),(-sin theta, cos theta)] then B=

If ((1+costheta+isintheta)/(sintheta+i+icostheta))^(4)=cosntheta+isinntheta then n=

For which value of an acute angle theta ,(i) ( cos theta )/( 1-sin theta ) +(cos theta )/( 1+sin theta ) =4 is true ? For which value of 0^(@) le theta le 90 ^(@) , above equation is not defined?

If 0lttheta ltpi/2,sin2theta=cos3theta then sintheta=