Suppose that x is a real number with `log_5(sinx) + log_5(cosx) = -1`. The value of `|sin^2xcosx + cos^2xsinx|` is equal to

lim_(xto pi//2) (sin(xcosx))/(cos(xsinx)) is equal to

Suppose that beta is a real number such that 3^(2x +3) = (3^(x))/(2^(x)) , then the value of 2^(-(1+log_(2)3)beta) is equal to

If log_(cosx)sinx+log_(sinx)cosx=2 , then x =

The value of lim_(xrarr0)(ln(2-cos15x))/(ln^(2)(sin3x+1)) is equal to

The value of lim_(xrarr0)(ln(2-cos15x))/(ln^(2)(sin3x+1)) is equal to

underset(xto pi//2)lim(sin(xcosx))/(cos(xsinx)) is equal to

underset(xto pi//2)lim(sin(xcosx))/(cos(xsinx)) is equal to

If log_(sinx)(cos x) = (1)/(2) , where x in (0, (pi)/(2)) , then the value of sin x is equal to-

If log_(sinx)(cos x) = (1)/(2) , where x in (0, (pi)/(2)) , then the value of sin x is equal to-

Let x be a positive real number such that sin(arctan\ (x)/(2))=(x)/(3) . The value of (log_(5)x) is equal to