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,
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and applying the definitions of the functions, tangent and cotangent
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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