NCERT 10TH STD MATH | TRIGONOMETRY | TRIGONOMETRIC IDENTITIES || FAQS || Shiksha Kendra || CHITTOOR
This video shows how to do a trigonometry problem that involves trigonometric identities.
Trigonometric identities are mostly memorised by students. But when they are posed with a problem involving proofs and trigonometric identities, students tend to find it difficult to solve. They fail to relate it with algebraic expressions. Algebra is as important as trigonometric formulas while it comes to solving expressions and proofs that involves trigonometric identities.
For example, the most commonly used algebraic expressions are (a+b)^2= a^2 + 2ab + b^2, (a-b)^2 = a^2 -2ab + b^2 and a^2 - b^2 = (a+b) (a-b). In these formulas, often we will have to substitute for sin theta and cos theta or any other trigonometric expression and then solve for proofs.
The trick lies in identifying these expressions and knowing when to use the algebraic expressions. Sometime, we will have to rationalise the denominator, take the LCM and find a common denominator to simple the expression. Then we will have to solve for the numerator. In such trigonometric problems where we are required to prove that the LHS = RHS, we have to take the LHS, use the algebraic expressions and simplify the expression to see if we get to the RHS. Once we have gotten the RHS, thus we get the proof.
In this problem, we are using, sin^2 theta + cos^2 theta =1. This is the only identity we are using.
This a a very simple problem. There are much more difficult topics in mathematics that involve algebraic expressions. One has to know algebra formulas and expressions better in order to solve these problems.