If `sec theta= x+1/(4x)` then `sec theta+ tan theta=` `(a) x, 1/(x), (b) 2x, 1/(2x), (c) -2x, 1/(2x), (d) -1/x, x`

If sin theta = x and sec theta = y , then tan theta is (a) xy (b) x/y (c) y/x (d) 1/(xy)

If 2 cos theta = x + (1)/(x), prove that 2 cos 3 theta = x ^(3) + (1)/(x ^(3)).

If f(x)=cos^2theta+sec^2theta, then f(x) f(x)>1 (d) f(x)geq2

If a chord joining P(a sec theta, a tan theta), Q(a sec alpha, a tan alpha) on the hyperbola x^(2)-y^(2) =a^(2) is the normal at P, then tan alpha is (a) tan theta (4 sec^(2) theta+1) (b) tan theta (4 sec^(2) theta -1) (c) tan theta (2 sec^(2) theta -1) (d) tan theta (1-2 sec^(2) theta)

i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x) , then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))

If cos theta = (2x)/(1+x^2) , find the values of sin theta and cot theta [Given x^2 lt 1 ]

If x = a cos theta and y = bcot theta, show that : (a^(2))/(x^(2)) - (b^(2))/ (y^(2)) = 1

If tan^(-1)x = theta , find the value of sin^(-1).(2x)/(1+x^(2))

If cos theta =1/2 (x+1/x ) , then 1/2(x^(2) +1/(x^(2))) is equal to :

The roots of the equation |(3x^(2),x^(2) + x cos theta + cos^(2) theta ,x^(2) + x sin theta + sin^(2) theta),(x^(2) + x cos theta + cos^(2) theta,3 cos^(2) theta,1 + (sin 2 theta)/(2)),(x^(2) + x sin theta + sin^(2) theta,1 + (sin 2 theta)/(2),3 sin^(2) theta)| = 0