If minimum value of term free from `x` for `(x/(sintheta) + 1/(xcostheta))^(16)` is `L_1` in `[pi/8,pi/4]` and `L_2` in `[pi/16,pi/8]`, then `L_2/L_1`

If L = sin^2 ((pi)/(16)) - sin^2 ( pi/8) and M = cos^2 ( (pi)/(16)) - sin^2 (pi/8), then :

The minimum value of function f(x) = 8^(sin^(-1)x)+8^(cos^(-1)x) is a) 2^(1+pi/4) b) 2^(-1+(3pi)/4) c) 2^(1+(3pi)/4) d) 2^(-1+(pi)/2)

The value of the expression 1+"cosec"(pi)/(4)+"cosec"(pi)/(8)+"cosec"(pi)/(16) is equal to

The value of the expression 1+"cosec"(pi)/(4)+"cosec"(pi)/(8)+"cosec"(pi)/(16) is equal to

In the expansion of ((x)/(costheta)+(1)/(xsintheta))^(16) , if l_(1) is the least value of the term independent of x when (pi)/(8) le theta le (pi)/(4) and l_(2) is the least value of the term independent of x when (pi)/(16) le theta le (pi)/(8) , then the value of (l_(2))/(l_(1)) is

In the expansion of ((x)/(costheta)+(1)/(xsintheta))^(16) , if l_(1) is the least value of the term independent of x when (pi)/(8) le theta le (pi)/(4) and l_(2) is the least value of the term independent of x when (pi)/(16) le theta le (pi)/(8) , then the value of (l_(2))/(l_(1)) is

In the expansion of ((x)/(costheta)+(1)/(xsintheta))^(16) , if l_(1) is the least value of the term independent of x when (pi)/(8) le theta le (pi)/(4) and l_(2) is the least value of the term independent of x when (pi)/(16) le theta le (pi)/(8) , then the value of (l_(2))/(l_(1)) is

In the expansion of ((x)/(costheta)+(1)/(xsintheta))^(16) , if l_(1) is the least value of the term independent of x when (pi)/(8) le theta le (pi)/(4) and l_(2) is the least value of the term independent of x when (pi)/(16) le theta le (pi)/(8) , then the value of (l_(2))/(l_(1)) is

The value of l = int _(-pi//2)^(pi//2) | sin x | dx is

The value of lim_(x to - pi) (int_(0)^(sin x)sin^(-1)t dt)/((x+pi)^(2)) is equal to L then find the value of 100 L :