The simplification of the expression 1-sec2x is equal to -tan2x. In this post, we will establish 1-sec^2x formula. We have: Let us now prove the above formulas. 1-sec2x Formula The formula of 1-sec2x is given below: $\boxed{1-\sec^2 x=-\tan^2 x}$ Proof: To simplify the expression $1-\sec^2 x$, we will follow the below steps: Step 1: We will … Read more
Note that cosx cosy is the product of two cosine functions cosx and cosy. The formula of the product cosx cosy is given as follows: cosx cosy = $\dfrac{\cos(x+y)+\cos(x-y)}{2}$ Proof of cosx cosy Formula Let us now prove the cosx cosy formula cosx cosy = $\dfrac{\cos(x+y)+\cos(x-y)}{2}$ Proof: We know that cos(x+y) = cosx cosy – … Read more
The simplification of the expression 1-cos2x is equal to sin2x. In this post, we will learn how to find the formula of 1-cos^2x. 1-cos2x Formula The formula of 1-cos2x is given below: 1-cos2x = sin2x 1-cos2x = sin2x Proof To prove $1-\cos^2x =\sin^2 x$, we will follow the below steps: Step 1: At first, we will … Read more
Cos3x formula in terms of cosx is as follows: 4cos3x-3cos x. In this post, we will also derive the cos3x formula in terms of sinx and give some examples. These formulas are very useful to solve trigonometric equations and simplify trigonometric expressions. Cos3x Formula Cos3x is the cosine function of a triple angle 3x. The … Read more
Tan2x formula in terms of tanx is as follows: $\dfrac{2\tan x}{1-\tan^2x}$. Here, we will also derive the tan2x formula in terms of sinx and cosx along with some examples. These formulas are very useful to solve trigonometric equations and simplify trigonometric expressions. Tan2x Formula Tan2x is the tangent function of a double angle 2x. The … Read more
Sin3x formula in terms of sinx is as follows: 3sinx – 4sin3x. The formula can be expressed as sine 3x = 3 sine x – 4 sine cube x. In this post, we will learn how to prove sin3x formula along with some examples. This is very useful in the area of Trigonometry to solve … Read more
Note that sin(cos-1 x) or sin(arc cosx) are algebraic functions, not trigonometric functions. The value of sin(cos-1 x) or sin(arc cosx) is equal to $\sqrt{1-x^2}$. In this post, we will simplify sin(cos^{-1} x). The formula of sin(cos inverse x) is given below: sin(cos-1 x) = root(1-x2). Simplify sin(cos-1(x)) We all know that $\sin(\cos^{-1}(x))= \sin(\text{arc} \cos … Read more
The value of cos(sin^-1(x)) or cos(arc sin x) is equal to $\sqrt{1-x^2}$. In this post, we will simplify the expression $\cos(\sin^{-1}(x))$. Simplify cos(sin-1(x)) We note that both $\cos(\sin^{-1}(x))$ and $\cos(arc \sin x)$ have the same value. Thus to find out the value of $\cos(\sin^{-1}(x))$ or $\cos(arc \sin x)$, let us put $\theta=\sin^{{-1}} x$ $\cdots (\star)$ … Read more
In this blog post, we will learn how to simplify the trigonometric expressions cos4 x -sin4 x and cos4x+sin4x. We will apply the following two trigonometric identities: cos4x-sin4x Formula To simplify the expression cos4 x -sin4 x, we first apply the formula a2-b2 =(a-b)(a+b) with $a=\cos^2x$ and $b=\sin^2x$. Therefore, $\cos^4x-\sin^4x$ $=(\cos^2x)^2 – (\sin^2 x)^2$ $=(\cos^2x-\sin^2x)(\cos^2x+\sin^2x)$ … Read more
The value of the expression 1-sin^2(x) is equal to cos^2(x). In this post, we will find the formula of 1-sin^2x. 1-sin2x Formula To simplify the expression 1 – sin2x, we will follow the below steps: Step 1: Let us apply the following Pythagorean trigonometric identity: 1 = sin2x + cos2x Step 2: Now, we substitute the above … Read more