Trigonometry
      Half angle formulas
      Trigonometric functions expressed by the cosine of the double angle
      Trigonometric identities, examples
Half angle formulas
Using the identities in which trigonometric functions are expressed by the half angle,
=>   =>  
and applying the definitions of the functions, tangent and cotangent 
=>   =>  
Trigonometric functions expressed by the cosine of the double angle
Replacing a/2 by a in the above identities, we get
         
Trigonometric identities examples
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  sin a + sin (a + 120) + sin (a + 240) = 0.   
Solution:   Applying the sum formula to the last two terms on the left side of the identity we get,
Example:   Prove the identity  
Solution:   Using the formula for the sum of the tangent 
Example:   Prove that  
Solution:  Replace sin a by cos (p/2 - a) and cos a by sin (p/2 - a) and use the sum to product formula
Trigonometry contents A
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