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) = $\dfrac{\tan a -\tan b}{1+\tan a \tan b}$ …(∗) 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) = $\dfrac{\tan x+\tan y}{1-\tan x \tan y}$. 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) ⇒ $\dfrac{\tan x+\tan y}{1-\tan x \tan y}$ … 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) = $\dfrac{\tan x+\tan y}{1-\tan x \tan y}$. 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) = $\dfrac{\tan x +\tan y+\tan z – \tan x \tan y \tan z}{1-\tan x \tan y-\tan y \tan z-\tan z \tan x}$. 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
The simplification of cos3x -sin3x is equal to cos3x -sin3x = (cosx -sinx)(2+sin2x)/2. The formula of cos^3x +sin^3x is given as follows: cos3x +sin3x = $\dfrac{(\cos x +\sin x)(2-\sin 2x)}{2}$. Formula of cos3x -sin3x Prove that cos3x -sin3x = (cosx -sinx)(2+sin2x)/2. Solution: Applying the formula a3 -b3 = (a -b)(a2+ab+b2), we get that cos3x -sin3x … Read more
The cot2x identity is given by cot2x = (cot2x-1)/2cotx. Note that cot2x is the cotangent of the angle 2x. The cot2x formula is as follows: cot2x = $\dfrac{\cot^2 x -1}{2 \cot x}$. Let us now learn how to prove the cot2x identity. Cot2x Formula in Terms of cotx The cot2x formula in terms of cotx … Read more
The cosec2x identity is given by cosec2x = (tanx + cotx)/2. That is, the formula of cosec 2x is equal to cosec 2x = $\dfrac{\tan x + \cot x}{2}$. Now, let us learn how to prove the cosec2x formula. Proof of cosec2x = (tanx+cotx)/2 Note that cosecx is the reciprocal of sinx. So we have … Read more
The value of sin(5pi/2) is equal to 1. The angle 5π/2 is equivalent to 450° and the value of sin 450° is equal to 1. The sin 5π/2 formula is given by $\sin \dfrac{5\pi}{2}=1.$ Let us learn how to find the value of sin(5pi/2). Value of Sin(5π/2) Answer: The value of sin 5π/2 is 1. … Read more