promath The formula or the identity of the product sinx cosy is obtained by the transformation of sums or differences of trigonometric angles. sinx cosy formula is given below. sinx cosy = $\dfrac{\sin(x+y)+\sin(x-y)}{2}$ Proof of sinx cosy Formula Let us now prove the sinx siny formula sinx cosy = $\dfrac{\sin(x+y)+\sin(x-y)}{2}$ Proof: It is known that sin(x+y) … Read more
The function sinx siny is the product of two sine functions sinx and siny. The formula or the identity of sinx siny is given as follows: sinx siny = $\dfrac{\cos(x-y)-\cos(x+y)}{2}$ Proof of sinx siny Formula We will now prove the sinx siny formula sinx siny = $\dfrac{\cos(x-y)-\cos(x+y)}{2}$ Proof: We know that cos(x+y) = cosx cosy … Read more
The general solution of tanx=tany for x is given by x=nπ+y where n= 0, ±1, ±2, ±3, …. In this post, we will learn how to find the general solution of tanx=tany as well as tanθ=tanα. Solutions of tanx = tany are given by x=nπ+y, n ∈ ℤ Let us now solve the trigonometric equation … Read more
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
Answer: The Laplace transform of t square is equal to 2/s3, that is, L{t2} = 2/s3. In this post, we will learn about the formula of L{t2} along with its proof. Laplace Transform of t2 Formula The Laplace of t square formula is given as follows L{t2} = 2/s3. Laplace Transform of t2 Proof We … Read more
The integration of xn is given as follows: ∫xndx = xn+1/(n+1) + C where C is an integration constant. In this post, we will learn how to find the integral of x to the power n. Integration of xn Formula The integration formula of xn (n-th power x) is given below: ∫xndx = xn+1/(n+1) + … Read more
The integration of root x + 1/root x is equal to 2/3 x3/2+2√x+C where C is an integral constant. In this post, we will learn how to integrate √x+1/√x. Integral of √x+1/√x Question: Find the integral $\int (\sqrt{x}+\dfrac{1}{\sqrt{x}})\ dx$ Answer: $\int (\sqrt{x}+\dfrac{1}{\sqrt{x}})\ dx$ = $\int \sqrt{x}\ dx$ + $\int \dfrac{1}{\sqrt{x}}\ dx$ by the sum rule … Read more
The modulus of x, that is, |x| is a continuous function. In this post, we will learn how to prove mod x is continuous. Let us now show that mod x is continuous at the point x=0. f(x)=|x| is continuous at 0 Let f(x)=|x|. Note that we have So we obtain that $\lim\limits_{x \to 0} … Read more