`([cos theta+i sin theta)/(sin theta+i cos theta))^(4)=?`

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

Using De Moivre 's theorem prove that : ((1+cos theta +i sin theta)/(1+cos theta - i sin theta))^n= cos n theta + i sin n theta , where i = sqrt(-1)

int (d theta)/((sin theta - 2 cos theta)(2 sin theta + cos theta))

The value of 3(cos theta-sin theta)^(4)+6(sin theta+cos theta)^(2)+4 sin^(6) theta is where theta in ((pi)/(4),(pi)/(2)) (a) 13-4cos^(4) theta (b) 13-4cos^(6) theta (c) 13-4cos^(6) theta+ 2 sin^(4) theta cos^(2) theta (d) 13-4cos^(4) theta+ 2 sin^(4) theta cos^(2) theta

If tan theta = p/q then (p sin theta - q cos theta)/(p sin theta + q cos theta)=

Prove that : (sin 5theta + sin 3theta)/(cos 5theta + cos 3theta) = tan 4theta

If theta lies in the first quadrant and 5 tan theta = 4 , " then " (5 sin theta - 3 cos theta )/( sin theta + 2 cos theta )=

If the coordinates of a variable point be (cos theta + sin theta, sin theta - cos theta) , where theta is the parameter, then the locus of P is

If theta in R - {(4n + 1) pi/4 , n in I} , then range of (cos 3 theta + sin 3 theta)/(cos theta - sin theta) is :

Prove the orthogonal matrices of order two are of the form [(cos theta,-sin theta),(sin theta,cos theta)] or [(cos theta,sin theta),(sin theta,-cos theta)]