0

Guest

Courses New

If f(x) =(sinx -sina) ÷(cosx-cosa), x≠a =1 , x=a is continuous, at x=a find a

If f(x) =(sinx -sina) ÷(cosx-cosa), x≠a
           =1            , x=a is continuous, at x=a find a

Grade:12

2 Answers

Arun
25750 Points
5 years ago
Dear student
 
for continuity Limit and value of function should be same.
 
Now f(a) = 1
 
limit x tends a f(x) = – tan a
 
hence a = – pi/4 
 
a can be other values too at which tan a = – 1
Bhagyashri verma
24 Points
5 years ago
Hi,
 
we know, sin A + sin B = 2 sin((A + B)/2) cos((A- B)/2)
and cos A - cos B = -2 cos((A + B)/2) cos((A- B)/2)
 
so, For function to be continuous limit x-> a f(x) = f(a)
hence, LHS
(sinx -sina) /div (cosx-cosa) = 2 sin((a+a)/2) cos(a-a)/2) / -2 cos(a+a)/2 cos(a-a)/2)
 
=-tan a
RHS f(a) =1 
for continuity lim x->a LHS = RHS hence  tan a = -1 
so, a = \pi /4
 
  

Think You Can Provide A Better Answer ?

Other Related Questions on IIT JEE Entrance Exam

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More