Question #dc296 Calculus Differentiating Trigonometric Functions Limits Involving Trigonometric Functions 1 Answer Cesareo R. Nov 24, 2016 See below. Explanation: #(cos^2x-cos^2y)/(x^2-y^2)=((cosx+cosy)/(x+y))((cosx-cosy)/(x-y))# so #lim_(x->y)(cos^2x-cos^2y)/(x^2-y^2)=lim_(x->y)((cosx+cosy)/(x+y))lim_(x->y)((cosx-cosy)/(x-y)) = (2cosy)/(2y)(-siny)=-(cosy siny)/y# but #sin(2y)=2cosy siny# so finally #-(cosy siny)/y=-sin(2y)/(2y)# Answer link Related questions How do you find the limit of inverse trig functions? How do you find limits involving trigonometric functions and infinity? What is the limit #lim_(x->0)sin(x)/x#? What is the limit #lim_(x->0)(cos(x)-1)/x#? What is the limit of #sin(2x)/x^2# as x approaches 0? Question #99ee1 What is the derivative of #2^sin(pi*x)#? What is the derivative of #sin^3x#? Question #eefeb Question #af14f See all questions in Limits Involving Trigonometric Functions Impact of this question 2434 views around the world You can reuse this answer Creative Commons License