Education Trigonometric and its inverse identities

An equation is called an identity when it is true for all values of the variables involved. Similarly an equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle(s) involved. List of trigonometric identities:

There are mainly two types of trigonometric identities, the primary identity and secondary identities. The primary trigonometric identity: The primary trigonometric identity is stated like this: Cos ^2 (A) + Sin^2 (A) = 1 Secondary trigonometric identity: The following secondary trigonometric identities are so called because they are derived from the primary trigonometric identity: (1) 1 + tan^2 (A) = sec^2 (A) (2) cot^2 (A) + 1 = cosec^2 (A) Besides these there can be many other tertiary trigonometric identities. We can solve trigonometric identities of tertiary types using these above three identities.Having problem with Calculating Standard Deviation keep reading my articles, i will try to help you. How to solve trigonometric identities? The best way to solve trigonometric identities is to convert them to basic function of sine or cosine. Then simplify if possible to the lowest form. Consider the following example to understand how complicated looking trigonometric identities can be easily solved using basic functions. Example: Prove the identity: sec (A)(1 – sin(A))(sec(A) + tan(A)) = 1 Solution: Left hand side = sec (A)(1 – sin(A))(sec(A) + tan(A)) = (1/cos A)(1 – sin A)(1/cos A + sin A/cos A) = (1 – sin A)(1 + sin A)/cos^2 (A) = (1 – sin^2 (A))/cos^2 (A) = cos^2 (A)/cos^2 (A) = 1 = Right hand side Inverse trigonometric identities: We know that every function has an inverse. A function has an inverse if and only if it is one to one and onto. Since all trigonometric functions are periodic, they are all many to one. So none of them can have an inverse. But if we restrict the domain suitably, it can be made one to one and then its inverse can also be defined. These inverse trigonometric functions also have identities. They are as follows: (1) sin^(-1) (x) + cos^(-1) (x) = Pi/2, x = 1 ---- domain restriction. (2) cosec^(-1) (x) + sec^(-1) (x) = Pi/2, x = 1 (3) tan^(-1) (x) + cot^(-1) (x) = Pi/2, x ? R The following relations between inverse trigonometric functions also need to be noted: (a) sin^(-1) (x) = cosec^(-1) (1/x); x ? [-1,1] – {0} (b) cos ^(-1) (x) = sec^(-1) (1/x); x ? [-1,1] – {0} (c) tan^(-1) (x) = cot ^(-1) (1/x); x>0 Know more about the Square Root Negative Number, online tutoring, Square Root of Negative Numbers. Online tutoring will help us to learn and do our homework very easily without going here and there.