Equation involving trigonometric function defined above are call trigonemtric
equation. Since we know that value of sin and cos function repeat after 2π
interval and value of tan function repeat after π interval.So there will be
infinite solution for these equations.We define two forms of solutions here

*Principle Solution:* The solution in the rangle 0 ≤ x ≤ 2π

*General Solution:* The expression involving integer n which gives all solutions
of a trigonometric equation is called the general solution.

**(a)**

sin x = 0 implies x = nπ, where n is any integer

cos x = 0 implies x = (2n + 1)(π/2)

**(b)**

sinx =siny then x=nπ+(-1)^{n}y where n is any integer

cosx=cosy then x=2nπ+y or x=2nπ- y where n is any integer

tanx=tany then x=nπ+y or x=nπ- y where n is any integer

1) Always try to bring the multiple angles to single angles using basic formla.Make sure all your angles are the same. Using sin(2X) and
sinX is difficult, but if you use sin2X = 2sin(x)cos(x), that leaves sin(x) and cos(x),
and now all your functions match.

The same goes for addition and subtraction: don't try
working with sin(X+Y) and sinX. Instead, use sin(X+Y) = sin(x)cos(y)+cos(x)sin(y) so that all
the angles match

2) Converting to sin and cos all the items in the problem using basic formula. I have mentioned sin and cos as they are easy to solve.You can use any other also.

3) Check all the angles for sums and differences and use the appropriate identities to remove them.

4) Use phythagorean identifies to simplfy the equations

5) Practice and Practice. You will soon start figuring out the equation and there symmetry to resolve them fast

Go Back to Class 11 Maths Home page Go Back to Class 11 Physics Home page

- Mathematics - Class 11 by RD Sharma
- NCERT Exemplar Problems: Solutions Mathematics Class 11
- NCERT Solutions: Mathematics Class 11th
- Mathematics Textbook for Class XI
- Cbse Mathematics for Class XI (Thoroughly Revised As Per New Cbse Syllabus)
- 37 Years Chapterwise Solved Papers (2015-1979): IIT JEE - Mathematics
- Play with Graphs - Skills in Mathematics for JEE Main and Advanced