For `x in (0,pi/2]`, the value of `log_b(sec^2 x+cosec^2 x)` where `b=tanx+cotx`, is (A) 1 (B) 2 (C) 3 (D) none

The value of int_0^(log5) (e^xsqrt(e^x-1))/(e^x+3)dx is (A) 3+2pi (B) 4-pi (C) 2+pi (D) none of these

Show that the least value of a^(2) sec^(2)x + b^(2) "cosec"^(2)x is (a+b)^(2) .

The value of int_(-pi/2)^( pi/2)(x^(3)+x cos x+tan^(5)x+1)dx is equal to (A)0(B)2C)pi(D) none of these

For x>=0, the smallest possible value of the expression,log_(2)(x^(3)-4x^(2)+x+26)-log_(2)(x+2) is ( A ) 1(B) 2(C)5(D) None of these

The minimum value of the function f(x)=3tanx+4cotx where x in(0,pi/2)

The minimum value oof f(x)=a^2sec^2x+b^2cosec^2x is (a+b)^2 and attained at tanx=sqrt(b//a)

cotx+tanx=2"cosec "x

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these