`(cos x)/(1-sin x)=tan(pi/4+(x)/(2))`

Evaluate the following limit: (lim)_(x->pi/4)(cos x-sin x)/((pi/4-x)(cos x+sin x))

Find the period of (a) (|sin4x|+|cos 4x|)/(|sin 4x-cos 4x|+|sin 4x+cos 4x|) (b) f(x)="sin"(pi x)/(n!)-"cos"(pi x)/((n+1)!) (c ) f(x)=sin x +"tan"(x)/(2)+"sin"(x)/(2^(2))+"tan"(x)/(2^(3))+ ... +"sin"(x)/(2^(n-1))+"tan"(x)/(2^(n))

Prove that : cos^(-1) x = 2 cos^(-1) sqrt((1+x)/(2)) (ii) Prove that : tan^(-1)((cosx + sin x)/(cosx - sin x)) = (pi)/(4)+ x

The expression (tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x)) simplifies to

If ((1+cos2x))/(sin2x)+3(1+(tanx)tan.(x)/(2))sin x=4 then the value of tanx can be equal to

Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the case: sin x = (1)/(4), x in II quadrant.

If A=(1)/(pi)[{:(sin^(-1)(pix),tan^(-1)((x)/(pi))),(sin^(-1)((x)/(pi)),cot^(-1)(pix)):}] and B=(1)/(pi) [{:(-cos^(-1)(pix), tan^(-1)((x)/(pi))),(sin^(-1)((x)/(pi)),-tan^(-1)(pix)):}] then A-B is equal to

If cos x + sin x = a , (- (pi)/(2) lt x lt - (pi)/(4)) , then cos 2 x is equal to

(cos(pi-x)cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^(2)x

Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^2x