If `sectheta=sqrt2` and `3(pi/2)``<``theta``<``2pi`, then evaluate `(frac(1+tantheta+cosectheta)(1+cottheta-cosectheta))`.

If tan theta + sectheta=sqrt3,0 < theta < pi, then theta is equal to............ A) pi/3 B) pi/6 C) (2pi)/(3) D) (5pi)/(6)

Derivative of tan^3 theta with respect to sec^3 theta at theta = ( pi /3) is ......... A) 1 B) ( sqrt 3 )/2 C) 0 D) - ( sqrt 3 )/2

Prove that: sqrt((1-sintheta)/(1+sintheta)) ={sectheta-tantheta} ,if -pi/2 = -sectheta+tantheta , if pi/2 < theta < (3pi)/2

Find the general solution of the following equation: sectheta = sqrt(2)

If theta in ((pi)/(2), (3pi)/(2)), then the value of sqrt(4 cos ^(4) theta + sin ^(2) 2 theta) + 4 cot theta cos ^(2) ((pi)/(4) -(theta)/(2)) is .............. A) -2 cot theta B) 2 cot theta C) 2 cos theta D) 2 sin theta

Select and write the correct answer from the given alternatives in each of the following: If tantheta= -4/3 , 3pi/2 < theta < 2pi ,then the value of 3sectheta+5tantheta is………..

Prove the following:if 2sin(theta+pi/3)=cos(theta-pi/6) ,then tantheta+sqrt3=0

If sin A = 1/sqrt10 and sin B =1/sqrt5 , where A and B are positive acute angles, then A + B is equal to.................. A) pi B) pi/2 C) pi/3 D) pi/4

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, eqautions of directrices and the length of latus-rectum of the hyperbola. : x=2sectheta, y=2sqrt3tantheta