Tangent Difference Identity
tan(A-B)=tanA-tanB/1+tanAtanB
The tangent difference identity is a trigonometric identity that describes the relationship between the tangent values of the difference of two angles. It can be stated as follows:
tan(x – y) = (tan x – tan y) / (1 + tan x tan y)
where x and y are angles in radians or degrees.
This identity can be used to simplify trigonometric expressions involving tangents of difference of angles. For example, if we have to find the value of tan(π/4 – π/6), we can use the tangent difference identity as follows:
tan(π/4 – π/6) = (tan π/4 – tan π/6) / (1 + tan π/4 tan π/6)
= [(1 – √3/3) – (√3/3)] / [1 + (1/3)]
= (1 – √3) / 2
Hence, we have simplified the expression using the tangent difference identity.
Another use of the tangent difference identity is in solving trigonometric equations. If we have an equation involving tangent functions, we can use the identity to transform it into an equation involving sines and cosines. This makes it easier to solve for the unknown angles.
More Answers:
Mastering The Double Angle Identity For Cosine And Its Sin EquivalentMastering The Double Angle Identity For Cosine In Mathematics.
Unlocking The Power Of Trigonometric Identity: The Double Angle Identity For Sin.