Show that the equation , ` sec theta + "cosec" theta = c ` has two roots between 0 and `2pi` , if ` c^2 lt 8`.

"cosec" theta =1/2

Show that cot theta +tan theta =sec theta cosec theta

Solve the equation cot((theta )/(2))-"cosec"((theta)/2)=cot theta

Find the minimum value of sec^2 theta + cos^2 theta + 2

Let a , b , c be nonzero real numbers such that int_0^1(1+cos^8x)(a x^2+b x+c)dx =int_0^2(1+cos^8x)(a x^2+b x+c)dx=0 Then show that the equation a x^2+b x+c=0 will have one root between 0 and 1 and other root between 1 and 2.

Show that (cosec theta -cot theta )^(2) =(1-cos theta )/( 1+cos theta )

P_1 and P_2 are the length of perpendicular from origin to the line x sec theta + y cosec theta =a and x cos theta - y sin theta = a cos 2 theta then ….... of the following is valid.

Equation of the line passing through the point ( a cos^(3) theta , a sin^(3) theta ) and perpendicular to the line x sec theta + y cosec theta = a is x cos theta - y sin theta = cos 2 theta .

If cos theta + sin theta = p and sec theta + cosec theta = q , prove that q (p^(2) - 1) = 2p .

Show that tan ^(2) theta +tan ^(4) theta =sec ^(4) theta -sec ^(2) theta