The sec2x identity is given by sec 2x = (sec2x cosec2x) / (cosec2x – sec2x). That is, the formula of sec2x is equal to sec 2x = $\dfrac{\sec^2x \cdot \text{cosec}^2x}{\text{cosec}^2x – \sec^2x}$ Now, let us learn how to find the sec2x identity Identity of sec2x Question: What is the identity of sec2x? Answer: The sec2x … Read more
The value of sin(3pi/2), that is, sin 270° is equal to -1. So the formula of sin(3π/2) is given by sin $\frac{3\pi}{2}$ = -1. Here we will learn how to find the value of sin 3pi/2. Note that Sin 3pi/2 Value Question: What is the value of sin(3pi/2)? Answer: sin(3π/2) is equal to -1. Explanation: … Read more
The cos^3x formula is given by cos3x = (cos3x + 3cosx)/4. In this post, we learn how to prove the cos cube x formula. What is cos cube x formula Answer: cos3x=(cos3x + 3cosx)/4 is the formula of cos cube x. Proof: We will follow the below steps in order to prove cos cube x … Read more
The sin cube x formula is given as follows: sin3x = (3sinx -sin3x)/4, that is, sin^3x formula is equal to (3sinx – sin3x) divided by 4. Here we establish the formula of sine cube x and give a proof. What is sin cube x formula Answer: sin3x = (3sinx -sin3x)/4 Proof: To establish the formula … Read more
Sin3x formula in terms of cosx is expressed as follows: sin3x = (4cos2x-1)√(1-cos2x). Here we learn how to prove sin3x formula in terms of cosine of x. sin3x in Terms of cos x In order to express sin3x formula in terms of cosx, we will use the following trigonometric formulae: Using the above formulas, we … Read more
The formula of cos^2x – sin^2x is equal to cos2x. Let us learn how to establish the proof the identity of cos2x-sin2x. cos2x-sin2x formula is given by cos2x-sin2x = cos2x. Proof of cos2x-sin2x Formula Question: Prove that cos2x-sin2x = cos2x. Proof: cos2x-sin2x = cosx ⋅ cosx – sinx ⋅ sinx = cos(x+x), here we have … Read more
The formula of cosh2x-sinh2x is given by cosh2x-sinh2x =1. Here we will learn how to prove cosh^2x-sinh^2x=1. Before we prove the identity cosh2x-sinh2x=1, let us recall that Proof of cosh^2x-sinh^2x=1 Question: Prove that cosh2x-sinh2x =1. Answer: By the above two formulas, we have that L.H.S = cosh2x – sinh2x = $\Big(\dfrac{e^x+e^{-x}}{2} \Big)^2$ $- \Big(\dfrac{e^x-e^{-x}}{2} \Big)^2$ … Read more
The sin(π/2-x) formula is given as follows: sin(π/2-x)=cosx …(∗) The formula of sin(pi/2-θ) is given by sin(π/2-θ)=cosθ. In this post, we will learn how to compute sin(pi/2-x) or sin(θ-pi/2). Proof of sin(pi/2-x) Formula To establish the above formula (∗), that is, the formula of sin(π/2-x), we need to apply the below formula: sin(a-b) = sina … Read more
For any x, sin(pi-x) formula is given below: sin(pi-x)=sinx Similarly, sin(pi-theta)=sin theta. In this post, we will learn how to compute sin(pi-x) or sin(pi-theta). sin(pi-x) Simplify To find the formula of sin(π-x), we will apply the following trigonometric identity: sin(A-B) = sinA cosB – cosA sinB …(∗) Here we put A=π and B=x; so that … Read more
The general solutions of sinx=-1 are given by x=(4n-1)π/2 where n is any integer. In this post, we will learn how to find the general solutions of the trigonometric equation sinx=-1. sinx=-1 General Solution Question: Find the general solutions of sinx= -1. Answer: As sin(-π/2)= -1, the equation sinx= -1 can be written sinx = … Read more