Trigonometry
      Sum to product and product to sum formulas or identities
         Sum to product formulas for the tangent and the cotangent functions
      The product to sum formulas for the sine and cosine functions
      Trigonometric identities, examples
Sum to product formulas for the tangent and the cotangent functions
From the definition of the function tangent,
or and
and for the function cotangent
or and
Using the same method,
and
The product to sum formulas for the sine and cosine functions
By adding and subtracting addition formulas derived are following product to sum formulas,
    and    
    and    
Trigonometric identities examples
Example:   Use,  tan 45 = 1 and  tan 60 = 3,  to prove that  tan 15 = 2 - 3.
Solution:
Example:   Verify the identity  
Solution:   We divide the numerator and denominator on the left side by sin a and to the right side we use the cotangent formula for the difference of two angles, thus
Example:   Express tan 3x in terms of tan x.
Solution:   Using the sum formula and the double angle formula for the tangent function,
Example:   Prove the identity  
Solution:
Example:   Prove the identity  
Solution:
Example:   If  tan a = 3/4, find tan a/2.   
Solution:   Use formula  to express tan a/2  in terms of  tan a.
Example:   Prove the identity  
Solution:   Substitute  then
Example:   Express the given difference  sin 61 - sin 59  as a product.   
Solution:   Since 
Example:   Prove the identity
Solution:   Using the formula for the sum of the tangent 
Trigonometry contents A
Copyright 2004 - 2020, Nabla Ltd.  All rights reserved.