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The cot(x+y) formula or the identity is given by cot(x+y) = $\dfrac{\cot x \cot y -1}{\cot x + \cot y}$. Here we will prove the formula of cot x+y. Proof of cot(x+y) Formula cot(x+y) = $\dfrac{\cot x \cot y -1}{\cot x + \cot y}$. Proof: Let us recall the following two formulas: sin(x+y) = sinx … Read more

The tan(x-y) is the tangent of the difference of the angles x and y. Tan(x-y) formula/identity is given as follows: tan(x-y) = $\dfrac{\tan x -\tan y}{1+\tan x \tan y}$. In this post, we will prove the formula of tan x-y. Proof of tan(x-y) Formula tan(x-y) = $\dfrac{\tan x -\tan y}{1+\tan x \tan y}$ Proof: We … Read more

The function cosx siny is the product of a cosine function and a sine function. In this post, we will learn how to prove the formula/identity of cosx siny. cosx siny Formula The cosx siny formula is given as follows: cosx siny = $\dfrac{\sin(x+y)-\sin(x-y)}{2}$ Let us now prove the above formula of cos x sin … Read more

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