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Grade: 12
        
If f(x) =(sinx -sina) ÷(cosx-cosa), x≠a
           =1            , x=a is continuous, at x=a find a
7 months ago

Answers : (2)

Arun
21012 Points
							
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
7 months ago
Bhagyashri verma
24 Points
							
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
 
  
7 months ago
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