Those who want to win!!

Hey! mathematicians who probably think that they have excelled in certain topics,surely would not be knowing this trick which i am going to discuss, do you have a guess? NO!

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WARNING!

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IN this article i have got something useful for all! OH! sorry only for Mathematicians.

You might be a expert in calculus or in algebra or even in geometry, trigonometry or so statistics but this post is for those who possibly find maths difficult when it comes to solving problems. Now for those who find calculus difficult, i have a perfect site for them, i would probably say  it is the best site right now in the network, which explains the basic of calculus in the efficient and intellectual way, what to say even an average student like me can understand. So what you are waiting for have a look at CALCULUS MADE EASY, but my dear friends now why to waste your time!, here is specially for you only, a trick to solve questions in which you probably are asked to give the value for the expressions made up of trigonometrical representations for a triangle and such questions are believed to be based on "solution of triangles" or "properties of triangle".

For Instance lets take an example, Find the value of

(a/c) sin2C + (c/a)sin2A. In This question a,c represent the sides of the triangle apposite to angle A and angle C respectively, as shown in the diagram below



Now to find the value for such expressions, some books or probably all books recommend to learn lengthy formulas for trigonometrical angles Like Sin(A/2) =((s-a)(s-b)/bc)^1/2

Where s  is called the semi perimeter of the triangle such that 2s = (a+ b+c), is the sum of lengths of sides of the triangle.

Now as i have promised you in the starting of the post to tell you the trick, here it is

For  sides a, c in the above example put a,c =1 and the angle A and angle C = 60⁰

That is simply consider the triangle as an equilateral triangle then putting the values  in the above example we get something like this (1/1)sin120⁰ + (1/1)sin120⁰ = 3^1/2

Personally i find this method as the best method to solve such type of questions if i have less time, but i would recommend to check your value using general method by putting in the formulas  for sin2C and sin2A , but obviously this is write method.

Here are few questions that you can attempt now,

Find the value for

1. (b/a)sin2A + (a/b)sin2B =
2. In a triangle ABC if, a, b, c are in A.P and cos$1 =( a/b+c) and cos$2 =(b/a+c) and cos$3=(c/a+b) , where $1,$2,$3 are angles then find the value of: tan²($1/2) +tan²($3/2)=

The answers to these question are 3^1/2 and 2/3, if you have got the answers you are on the way to success!!!

Have fun

With Regards!

Posted in: maths,tricks