varepsilon^(prime prime2)" Evaluate "tan((1)/(2)sin^(2)(3)/(4))

if tan(2a-3b)*tan(4b-a)=1a,b varepsilon(0,(pi)/(2)) then the value of tan((a+b)/(6))

Find the prime factors of.(1)60(2)72(3)32

Evaluate the following: (i) tan{2\ tan^(-1)(1/5)-pi/4} (ii) tan(1/2\ sin^(-1)(3/4)

Evaluate the following: (i) tan{2\ tan^(-1)(1/5)-pi/4} (ii) tan(1/2\ sin^(-1)(3/4)

Area of the triangle formed by the threepoints 't_(1)^(prime)*'t_(2)^(prime) and 't_(3)^(prime) on y^(2)=4ax is K|(t_(1)-t_(2))(t_(2)-t_(3))(t_(3)-t_(1))| then K=

Let U" "=" "{1," "2," "3," "4," "5," "6," "7," "8," "9} , A" "=" "{1," "2," "3," "4} , B" "=" "{2," "4," "6," "8" "} and C" "=" "{" "3,4," "5," "6" "} . Find (i) A^(prime) (ii) B^(prime) (iii) (AuuC)^(prime) (iv) (AuuB)^(prime) (v) (A^

If sum of all the solutions of the equation (4tan x+tan^(2)x+1)=2sqrt(2)sin(x+(pi)/(4))(1+tan^(2)x) in [0,pi] is (p, (pi)/(q)) where p,q are relatively prime number, then find the value of (p+q)

If f(x)=(x+3)/(5x^2+x-1) and g(x)=(2x+3x^2)/(20+2x-x^2) such that f(x) and g(x) are differentiable functions in their domains, then which of the following is/are true (a) 2f^(prime)(2)+g^(prime)(1)=0 (b) 2f^(prime)(2)-g^(prime)(1)=0 (c) f^(prime)(1)+2g^(prime)(2)=0 (d) f^(prime)(1)-2g^(prime)(2)=0

Find the minimum prime number which divides 9^(1)+81^(2)+243^(3)+2187^(4)

If x^2+y^2=R^2(w h e r eR >0)a n dk=(y prime prime)/(sqrt((1+yprime^2)^3)) then find k in terms of R alone.