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

If "cosec" theta = sqrt(5) , find the value of (i) 2-sin^(2)theta - cos^(2)theta (ii) 2 + (1)/(sin^(2)theta) - (cos^(2)theta)/(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) then the difference between maximum and minimum values of u^(2) is

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))

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

Complete the following activity by filling the boxes sin^(2) theta+cos^(2) theta=square ……….(Identity) Dividing each term by cos^(2)theta (sin^(2)theta)/(cos^(2)theta)+(cos^(2)theta)/(cos^(2)theta)=(square)/(cos^(2)theta) :.square+1=square

Show that the maximum and minimum values of sqrt(a^(2)cos^(2)theta + b^(2)sin^(2) theta) + sqrt(a^(2)sin^(2)theta + b^(2)cos^(2)theta) are sqrt(2(a^(2) +b^(2)) and a + b respectively.

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

Prove the following identities: sin^(8)theta+cos^(8)theta=(sin^(2)theta-cos^(2)theta)(1-2sin^(2)theta cos^(2)theta)