Trigonometry XI


   
 
Sum Formula
For any two angles A and B, we have
 
 
 
 
 
Difference Formula
 
For any two angles A and B we have
 
 
 
 
 
For any two angles A and B
 
(i) sin(A + B) sin(A - B) = sin2A - sin2B = cos2B - cos2A
 
(ii) cos(A + B) cos(A - B) = cos2A - sin2B = cos2B - sin2A
 
[The proofs of the above identities are same as for Circular functions]
 
Products of functions in terms of Sums and differences and
 
vice-versa
 
 
 
By adding (a) and (b) we get
 
 
Putting A + B = C and A - B = D
 
 
By subtracting (b) from (a) we get
 
 
Putting A + B = C and A - B = D
 
 
 
 
By adding (c) and (d) we get
 
 
Putting A + B = C and A - B = D
 
 
by subtracting (d) from (c) we get
 
 
Putting A + B = C and A - B = D
 
 
Summary of above results
 
 
 
 
 
 
 
 
 
 
 
  
     
   
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