lim_(alpha rarr(pi)/(4))(sin alpha-cos alpha)/(alpha-(pi)/(4))

The value of (sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha is

The value of (sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha is

The value of (sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha is

Prove that lim_(x rarr4)((cos alpha)^(x)-(sin alpha)^(x)-cos2 alpha)/(x-4)=cos^(4)alpha ln(cos alpha)-sin^(4)alpha,alpha in(0,(pi)/(2))

The expression (sin alpha+cos alpha)/(cos alpha-sin alpha) tan((pi)/(4)+alpha)+1, alpha in (-(pi)/(4), (pi)/(4)) simplifies to :

The expression (sin alpha+cos alpha)/(cos alpha-sin alpha) tan((pi)/(4)+alpha)+1, alpha in (-(pi)/(4), (pi)/(4)) simplifies to :

Let f(x) be defined as f(x)=max{a,b,c} where a=lim_(n rarr oo)lim_(alpha rarr1^(+))(alpha^(n)|sin x|+|cos x| alpha^(-n))/(alpha^(n)+alpha^(-n)) , b=lim_(n rarr oo)lim_(alpha rarr1^(-))(alpha^(n)|sin x|+|cos x| alpha^(-n))/(alpha^(n)+alpha^(-n)) , c=lim_(n rarr oo)(pi)/(4n)[1+cos(pi)/(2n)+...+cos((n-1)pi)/(2n)] then The range of f(x) is

Calculate cos ((alpha)/(2)) if sin alpha=4/5 and alpha alpha in ((-3pi)/(2),-pi)

lim_(x rarr0)(sin(alpha+x)-sin(alpha-x))/(cos(alpha+x)-cos(alpha-x))