(cos45^(@))/(x^(2)+cos alpha x^(2))

If int ((x cos alpha+1)dx)/((x^(2)+2x cos alpha+1)^(3//2))=(f(x))/(sqrt(x^(2)+2x cos alpha+ 1))+c then f(x)=

lim_(x rarr0)(sin(alpha+beta)x+sin(alpha-beta)x+sin2 alpha x)/(cos^(2)beta x-cos^(2)alpha x)

cos^(2) ( 45^(@) - alpha ) + cos^(2) (15^(@) + alpha ) - cos^(2)(15^(@)-alpha)=

If beta is such that sin beta!=0 then show that (x^(2)+2x cos2 alpha+1)/(x^(2)+2x cos2 beta+1)x in R always lies between (cos^(2)alpha)/(cos^(2)beta) and (sin^(2)alpha)/(sin^(2)beta)

If cos^(-1)x-"cos"^(-1)(y)/(2)=alpha , then 4x^(2)-4xy cos alpha+y^(2) is equal to :