If `theta=3alpha`and `sintheta=a/(sqrt(a^2+b^2)),` the value of the expression `acos e calpha-bsecalpha` is (a)`a/(sqrt(a^2+b^2))` (b) `2sqrt(a^2+b^2)` (c) `a+b` (d) none of these

If theta=3alpha and sin theta=(a)/(sqrt(a^(2)+b^(2)) , the value of the expression a co sec alpha-b sec alpha is

(a) a^2+b^2 (b) a+b (c) a^2-b^2 (d) sqrt(a^2+b^2)

If sintheta = a/ (sqrt(a^2+b^2)) , 0< theta<90^@ , find the values of costheta and tantheta

IfI=int(dx)/((a^2-b^2x^2)^(3/2)),t h e nIe q u a l (a) x/(sqrt(a^2-b^2x^2))+C (b) x/(2sqrt(a^2-b^2x^2))+C (c) (a x)/(sqrt(a^2-b^2x^2))+C (d) none of these

If acostheta-bsintheta=c , then asintheta+bcostheta= (a) +-sqrt(a^2+b^2+c^2) (b) +-sqrt(a^2+b^2-c^2) (c) +-sqrt(c^2-a^2-b^2) (d) None of these

If asinx+bcos(x+theta)+bcos(x-theta)=d , then the minimum value of |costheta| is equal to (a) 1/(2|b|)sqrt(d^2-a^2) (b) 1/(2|a|)sqrt(d^2-a^2) (c) 1/(2|d|)sqrt(d^2-a^2) (d) none of these

If sin alpha+sin beta=a\ a n d\ cosalpha-cosbeta=b , then tan(alpha-beta)/2= -a/b b. b/a c. sqrt(a^2+b^2) d. none of these

The solution for x of the equation int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2 is pi (b) (sqrt(3))/2 (c) 2sqrt(2) (d) none of these

If a variable straight line x cos alpha+y sin alpha=p which is a chord of hyperbola (x^(2))/(a^(2))=(y^(2))/(b^(2))=1 (b gt a) subtends a right angle at the centre of the hyperbola, then it always touches a fixed circle whose radius, is (a) (sqrt(a^2+b^2))/(ab) (b) (2ab)/(sqrt(a^2+b^2)) (c) (ab)/(sqrt(b^2-a^2)) (d) (sqrt(a^2+b^2))/(2ab)

Consider the equation sec theta +cosec theta=a, theta in (0, 2pi) -{pi//2, pi, 3pi//2} If the equation has four distinct real roots, then (a) |a| gt 2sqrt(2) (b) |a| lt 2sqrt(2) (c) a ge -2sqrt(2) (d) none of these