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 How To Do Trigonometry
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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. Basic Formulas Suppose we have two function of 'x' that is 'u' and 'v', where 'a' and 'n' are constants, and 'd' is the differential operator. Let’s see basic general rule: Linearity rule: (d/dx) (a u) = a (du/dx) Addition rule: (d/dx) (u+v) = du/dx + dv/dx Subtraction rule: (d/dx) (u -v) = du/dx – dv/dx Product rule: (d/dx) (u *v)= u dv/dx + v du/dx
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Hyperbolic trigonometry formulas Hyperbolic functions are analog of the trigonometric functions. The basic hyperbolic functions are the hyperbolic "sinh" and the hyperbolic cosine "cosh" from which, several other functions are derived like hyperbolic tangent "tanh", and many more derived trigonometric functions. Hyperbolic trig functions, are defined using ex and e–x. Rules of Differentiation Differentiation is a process used to find a derivative of function where derivative means rate of change with respect to some variable like derivative of f(x) with respect to 'x' is d (f(x) dx
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