If `A=([sin theta,cos theta],[-cos theta,sin theta])` then `|A|` is

If A=[[sin theta,cos theta-cos theta,sin theta]] then A^(2)=

(sin theta)/(1-cos theta)=(1+cos theta)/(sin theta)

If A= [[cos theta,-sin theta],[sin theta,cos theta]] ,then Adj A is (a) [[cos theta,-sin theta],[cos theta,sin theta]] (b) [[1,0],[0,1]] (c) [[cos theta,sin theta],[-sin theta,cos theta]] (d) [[-1,0],[0,-1]]

If A(theta)=[(sin theta, i cos theta),(i cos theta, sin theta)] , then which of the following is not true ?

Consider f(theta)=|[sin theta,cos theta,sin theta],[cos theta,sin theta,cos theta],[cos theta,sin theta,sin theta]| then A) f(theta)=0 has exactly 2 real solutions in [0,pi] B) f(theta)=0 has exactly 3 real solutions in [0,pi] C) Range of function (f(theta))/(1-sin2 theta) is [-sqrt(2),sqrt(2)] D) Range of function (f(theta))/(sin2 theta-1) is [-3,3]

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)]

If theta^(@) lt theta lt 90^(@) and (sin theta)/(cos theta) + (cos theta)/(sin theta)=2 , then which of the following is equal to theta ?

(1-sin theta)/(cos theta)-(cos theta)/(1+sin theta)=2tan theta