1-sinx Formula, Proof | 1+sinx Identity

The 1-sinx formula is given by 1-sinx= [cos(x/2) -sin(x/2)]2. The 1 plus sinx idenity is given as follows: $1+\sin x =(\cos \frac{x}{2}+\sin \frac{x}{2})^2$. Let us now find the formula of 1-sinx and 1+sinx. Formula of 1-sinx Answer: 1-sinx= $(\cos \frac{x}{2}-\sin \frac{x}{2})^2$. Explanation: To find the formula of 1-sinx, we will use the following two trigonometric … Read more

1-cosx Identity, Proof | 1-cosx Formula [in terms of sin]

The 1-cosx identity is given by 1-cosx= 2sin2(x/2). 1 minus cosx is a trigonometric expression and its formula is given below: $1-\cos x =2 \sin^2 (\frac{x}{2})$. Let us now find the formula of 1-cosx in terms of sin. 1-cosx Formula in Terms of Sin Answer: 1-cosx formula in terms of sin is equal to 1-cosx= … Read more

Cot(a+b) Cot(a-b) Formula, Proof

Cot(a+b) Cot(a-b) can be expressed in terms of cot as well as tan. In this post, we will learn to find cot(a+b)cot(a-b) formula with proof. Let us now find the formula of the product cot(a+b) and cot(a-b). Cot(a+b) Cot(a-b) Formula in Terms of Cot Using the identities of cot(a+b) and cot(a-b), the given expression can … Read more

Find the Values of sin18, cos18

The value of sin18° is equal to (√5-1)/4 and the value of cos18° is equal to √(10+2√5)/2. Here we will learn to find the values of sin18, cos18. The sin 18 degree formula is given by $\boxed{\sin 18^\circ = \dfrac{\sqrt{5}-1}{2}}$ The cos 18 degree formula is given by $\boxed{\cos 18^\circ = \dfrac{\sqrt{10+2\sqrt{5}}}{2} }$ Value of … Read more

Find Value of sin(3pi/4) | Sin 3π/4 Value

The value of sin(3pi/4) is equal to 1/√2. As the angle 3π/4 is same as 135° in degrees, the value of sin135° is 1/√2. The sin 3π/4 formula is given as follows $\boxed{\sin \dfrac{3\pi}{4}=\dfrac{1}{\sqrt{2}} }$ Let us learn how to find the value of sin(3pi/4). Value of Sin(3π/4) Answer: The value of sin 3π/4 is … Read more

Cos minus theta is equal to cos theta: Proof

Cos minus theta is equal to cos theta, that is, cos(-θ) = cosθ. Similarly, cos(-x) = cosx. In this post, we learn to find the value of cos of minus theta. The cos minus theta formula is given as follows: cos(-θ) = cosθ. Prove that cos(-theta) = cos theta We will follow the below steps … Read more

Sin(90-theta) Formula, Proof | Simplify Sin(θ-90)

The sin(90-theta) formula is given by sin(90-θ) = cosθ. As 90°=π/2, sin(90-θ) formula can be written as follows: sin(π/2-θ) = cosθ. On the other hand, sin(θ-90) formula is given by sin(θ-90) = -cosθ. Let us now simplify the expression sin(90-theta). Simplify Sin(90-theta) Question: Simplify the expression sin(90-θ). Answer: To simplify the expression sin(90-θ), we will … Read more

tan(pi-x) Formula | Simplify tan(x-π)

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

If x+y=π/4, then prove (1+tanx)(1+tany)=2

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