promath

The tan(π-x) formula is given by tan(π-x)= -tanx. The formula of tan(pi-θ) is equal to tan(π-θ)= -tanθ. In this post, we will learn how to compute tan(pi-x) and tan(θ-pi). Note that Proof of tan(pi-x) Formula Let us use the formula: tan(a-b) = ${\displaystyle \frac{\tan a-\tan b}{1+\tan a\tan b}}$ …(∗) Put a=π, b=x. Thus, we … Read more

In this post, we will prove (1+tanx)(1+tany)=2 when x+y is equal to π/4 =45°. To prove this, we will use the following formula: tan(x+y) = ${\displaystyle \frac{\tan x+\tan y}{1-\tan x\tan y}}$. Question: If x+y=π/4, then prove that (1+tanx)(1+tany)=2. Solution: Step 1: Given that x+y=π/4. Therefore, tan(x+y) = tan(π/4) ⇒ ${\displaystyle \frac{\tan x+\tan y}{1-\tan x\tan y}}$ … Read more

In this post, we will prove tanx + tany + tanz = tanx tany tanz when x+y+z is equal to π. Here we will use the following formula: tan(x+y) = ${\displaystyle \frac{\tan x+\tan y}{1-\tan x\tan y}}$. Question: If x+y+z=π, then prove that tanx + tany + tanz = tanx tany tanz. Solution: Given that x+y+z=π. … Read more

The formula of tan(x+y+z) is given as follows: tan(x+y+z) = ${\displaystyle \frac{\tan x+\tan y+\tan z–\tan x\tan y\tan z}{1-\tan x\tan y-\tan y\tan z-\tan z\tan x}}$. In this post, let us learn how to prove the formula of tan(x+y+z). Proof of tan(x+y+z) Formula We will use the formula tan(a+b) = … Read more

The cos(x+y+z) formula is given by cos(x+y+z) = cosx cosy cosz – sinx siny cosz – sinx cosy sinz – cosx siny sinz. Here we establish the identity of cos(x+y+z). Formula of cos(x+y+z) The formula of cos(x+y+z) is given below: $\cos(x+y+z) = \cos x \cos y \cos z – \sin x \sin y \cos z … Read more

The sin(x+y+z) identity is given by sin(x+y+z) = sinx cosy cosz + cosx siny cosz + cosx cosy sinz – sinx siny sinz. In this post, we will establish the formula of sin(x+y+z). Formula of sin(x+y+z) The formula of sin(x+y+z) is given as follows: $\sin(x+y+z) = \sin x \cos y \cos z + \cos x … Read more