Simplifying Trig Expressions Simplifying Trig Expressions
Today, we will learn how to simplify trig expressions, for understating the concept of simplify trig expressions we need to have knowledge of trigonometric functions. So, for simplifying trig expression we will go through some examples. Example 1: Simply the equation given as cotx/cosecx ? Solution: cotx/cosecx, For simplifying this type of equation we just need to convert the trigonometric variable into simplest form and do some very simple operation on them. = cotx/cosecx, We can write, = cotx as 1/tanx, and = cosecx as 1/sinx, so put this value in the above equation and we will get: = (1/tanx )/ (1/sinx), Now, tanx can be written as sinx/cosx, on putting this value in the above equation as: = 1/(sinx/cosx) / (1/sinx), Now, we need to take LCM as sinx. We can rewrite the equation as: = cosx/sinx *sinx, Now, sinx gets cancel with sinx and we will get the required answer as cosx. Know More About Properties Of Irrational Numbers
Tutorcircle.com
Page No. : 1/4
As you can see cotx/cosex are simplified as cosx in this way, any big expression can be simplified. So, the required equation can be simplified as cosx. Example 2: Simply the equation given as: cotx +tanx ? Solution: cotx + tanx, cotx can be written as 1/tanx, So we can rewrite the given equation as: = 1/tanx +tanx, Now, tanx can be written as sinx /cosx, = 1/(sinx/cosx) + sinx /cosx, = cosx/sinx +sinx/cosx, Now, on taking LCM we will get: = Cos2x+sin2x/cosx*sinx, Now, we can write sin2x +cos2x=1, So, we can write problem as: = 1/cosx*sinx, = 1/cosx *1/sinx, = secx *cosecx, So, the required equation can be simplified as secx *cosecx. Example 3: Simply the equation cotx + 1 / cosecx ? Solution: cotx can be written as 1/tanx, and tanx can be written as sinx/cosx, So, we can write cotx as cosx/sinx and we can write cosecx as 1/sinx. Now, put all these values in the given equation we will get: = (cosx /sinx) +(1/1/sinx), We can write this equation as: = (cosx +sinx ) * sinnx *1/sinx, So, sinx gets cancel with sinx and we will get, = cosx + sinx, So, the above equation can be simplified as cosx + sinx.
Read More About Is A Repeating Decimal A Rational Number
Tutorcircle.com
Page No. : 2/4
Example 3 :Simplify the following trigonometric expression. [sec(x) sin 2x] / [1 + sec(x)] Solution to Question 3: Substitute sec (x) that is in the numerator by 1 / cos (x) and simplify. [sec(x) sin 2x] / [1 + sec(x)] = sin 2x / [ cos x (1 + sec (x) ] = sin 2x / [ cos x + 1 ] Substitute sin 2x by 1 - cos 2x , factor and simplify. = [ 1 - cos 2x ] / [ cos x + 1 ] = [ (1 - cos x)(1 + cos x) ] / [ cos x + 1 ] = 1 - cos x
Tutorcircle.com
Page No. : 2/3 Page No. : 3/4
Thank You
TutorCircle.com