**MATHMAA**

General Solutions is a topic in Trigonometry, the formula related to General Solutions are provided in this math-formula-sheet-generalSolutions. These formula will help the students who are in 10th, 11th, 12th and College Grade too.

In this we get Principal Value and General solution of the angle.

** PRINCIPAL SOLUTIONS:**

The solutions of a trigonometric equations for which 0\(\leq x< 2\prod\) are called ** Principal solutions**.

**GENERAL SOLUTIONS:**

The expressions involving integer 'n' which gives all solutions of a Trigonometric equation is called the "** general solution**".

Principal Value and General solution of Sin, Cos, Tan as follows:

1) If Sin(x)= 0

Principal value of x = 0 as Sin(x)=Sin(0)

General solution of x = n\(\prod\), n\(\epsilon Z\), Z is set of integers.

2)If Cos(x)=0 then

Principal value of x =\(\frac{\prod}{2}\)

General Solution of x = (2n+1)\(\frac{\prod}{2}\).

3)If Sin(x)=Sin(y) then

Principal value of x = y and

General Solution of x = \(n\prod+(-1)^{n}y\), where n\(\epsilon Z\)

4) If Cos(x)= Cos(y) then

Principal value of x = y and

General Solution of x =\(2n\prod\pm y\), where n\(\epsilon Z\).

5)If Tan(x)= Tan(y) then

Principal value of x=y and

General solution of x =\(n\prod+y\)., where \(n\epsilon Z\).

6) If \(Sin^{2}(x)=Sin^{2}(y)\), or \(Cos^{2}(x)=Cos^{2}(y)\) , or \(Tan^{2}(x)=Tan^{2}(y) \)then

Principal value of x=y and

General solution of x= \(n\prod \pm y\). , \(n\epsilon Z\).

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