`(2sin^2 ( theta /2))/(cos^2 (theta/2))`

The value of the determinants |("cos"^(2)(theta)/(2),"sin"^(2)(theta)/(2)),("sin"^(2) (theta)/(2),"cos"^(2) (theta)/(2))| for all values of theta , is :

The value of the determinant |{:("cos"^(2)(theta)/(2),"sin"^(2)(theta)/(2)),("sin"^(2)(theta)/(2),"cos"^(2)(theta)/(2)):}| for all values of theta , is

17*cos^(4)theta-sin^(4)theta is equal to (a)1-2sin^(2)((theta)/(2))(b)2cos^(2)theta-1(c)1+2sin^(2)((theta)/(2))(d)1+2cos^(2)theta

int_ (0) ^ ((pi) / (2)) sin theta cos theta (a ^ (2) sin ^ (2) theta + b ^ (2) cos ^ (2) theta) ^ ((1) / ( 2)) d theta = ((1) / (3)) ((a ^ (2) + ab + b ^ (2)) / (a + b))

Prove each of the following identities : (sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = (2) /((sin^(2) theta - cos^(2) theta)) = (2) /((2sin^(2) theta -1))

Prove the following identities: ((1+sin theta)^(2)+(1-sin theta)^(2))/(cos^(2)theta)=2((1+sin^(2)theta)/(1-sin^(2)theta))

u=sqrt(a^(2)cos^(2)theta+b^(2)sin^(2)theta)+sqrt(a^(2)sin^(2)theta+b^(2)cos^(2)theta^(2)) then the difference between the maximum and minimum values of u^(2) is given by : (a) (a-b)^(2) (b) 2sqrt(a^(2)+b^(2))(c)(a+b)^(2) (d) 2(a^(2)+b^(2))

(sin ^ (4) theta + cos ^ (4) theta) / (1-2sin ^ (2) theta cos ^ (2) theta) = 1

If z=1-cos theta+i sin theta, then |z|=2(sin theta)/(2) b.2(sin theta)/(2)c.2|(sin theta)/(2)|d.2|(cos theta)/(2)|