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 