The two legs of a right triangle are `sin theta +sin ((3pi)/2-theta)` and `cos theta -cos( (3pi)/2-theta)` The length of its hypotenuse is

Vertices of a variable triangle are (3, 4), (5 cos theta, 5 sin theta) and (5 sin theta, -5 cos theta) , where theta in R . Locus of its orthocentre is

sin^(4) theta + cos ^(4) theta + 2sin^(2) theta cos ^(2) theta has value 1.

If sintheta + sin^(2)theta = 1 , prove that cos^(2)theta + cos^(4)theta = 1

The diameter of the nine point circle of the triangle with vertices (3, 4), (5 cos theta, 5 sin theta) and (5 sin theta, -5 cos theta) , where theta in R , is

sintheta = (3)/5 , (pi)/2 lt theta lt pi sin2theta = (-12)/25

If tan((pi)/(2) sin theta )= cot((pi)/(2) cos theta ) , then sin theta + cos theta is equal to

The maximum value of the expression 1/(sin^2 theta + 3 sin theta cos theta + 5cos^2 theta) is

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

The length of normal to the curve x=a(theta+sin theta), y=a(1-cos theta), at theta=(pi)/(2) is

Show that (1)/( cos theta ) -cos theta =tan theta .sin theta