" If "(sin theta)/(x)=(cos theta)/(y)+" then "sin theta-cos theta" is "

If (sin theta)/(x)=(cos theta)/(y) , then show that sin theta-cos theta=(x-y)/( sqrt(x^(2)+y^(2))) .

If (sin theta) (x) = (cos theta)/(y) , then prove that sin theta - cos theta = (x - y)/(sqrtx^2 + y^2) .

If tan theta = (x)/(y) , " then " (x sin theta + y cos theta)/( x sin theta - y cos theta) is equal to

If the system of linear equations {:((cos theta)x + (sin theta) y + cos theta=0),((sin theta)x+(cos theta)y + sin theta=0),((cos theta)x + (sin theta)y -cos theta=0):} is consistent , then the number of possible values of theta, theta in [0,2pi] is :

If the system of linear equations {:((cos theta)x + (sin theta) y + cos theta=0),((sin theta)x+(cos theta)y + sin theta=0),((cos theta)x + (sin theta)y -cos theta=0):} is consistent , then the number of possible values of theta, theta in [0,2pi] is :

If R(theta) = [(cos theta, sin theta),(sin theta, -cos theta)] Write:- R(x +y).

For different values of theta, the locus of the point of intersection of the straight lines x sin theta-y(cos theta-1)=a sin theta and x sin theta-y(cos theta+1)+a sin theta=0 represents

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

If (sin theta+cos theta)/(sin theta-cos theta)=3 then sin^4 theta-cos^4 theta=

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