Evaluate the value of `("lim")_(nvecpi/2)tan^2xsqrt((2sin^2x+3sinx+4)-sqrt(sin^2x+sinx+2))`

Evaluate lim_(xto pi//2) tan^(2)xsqrt(2sin^(2)x+3sinx+4)-sqrt(sin^(2)x+6sinx+2).

The value of lim_(x rarr(pi)/(2))tan^(2)x(sqrt(2sin^(2)x+3sin x+4)-sqrt(sin^(x)+6sin x+2)) is equal to

intcosx/sqrt(sin^2x+3sinx+4)dx

(cos x)/(sqrt(sin^(2)x-2sinx-3))

Evaluate the following limits (i) lim_(x to (pi)/(2)) tan^(2) x [sqrt(2 sin^(2) x + 3 sin x + 4) - sqrt(sin^(2) x + 6 sin x + 2)] (ii) lim_(theta to 0) (sqrt(1 + sin 3 theta) -1)/(ln(1 + tan 2theta)) (iii) lim_(x to 0) (sqrt(1 + x) - ""^(3)sqrt(1 + x))/(x) (iv) lim_(phi to 0) (8)/(phi^(8)) (1 - cos (phi^(2))/(2) - cos (phi^(2))/(4) + cos (phi^(2))/(2). cos (phi^(2))/(4))

int(cosx)/(sqrt(sin^2x-sinx-3))dx=

int(cosx)/(sqrt(sin^2x-2sinx+5))dx=

(cosx-sinx)/(sqrt(8-sin2x))

The value of lim_(xrarrpi//2)12 tan^(2)x[sqrt(6+3 sin x-2cos^(2)x)-sqrt(3+6 sin x-cos^(2)x)] is _____________

Evaluate the following limits: lim_(xrarr pi//6)((2sin^(2)x+sinx-1))/((2sin^(2)x-3sinx+1))