limit (1-tanx)/(sinx-cosx) as x approaches pi/4
📐 In this video, we'll be finding the limit of (1 - tan x) / (sin x - cos x) as x approaches pi/4. 🔎 We'll be using algebraic manipulation to simplify the expression and make it easier to find the limit.
🔍 To start, we'll rewrite the expression using the identity for tangent as sine over cosine. We'll then distribute cosine in the numerator and simplify. Finally, we'll use the fact that cosine x minus sine x and sine x minus cosine x are equivalent expressions to simplify the expression even further.
📝 Our final answer will be -√2. We'll show how we arrived at this answer step by step.
🤔 Do you struggle with finding limits? 🤔 Not sure how to use algebraic manipulation to simplify expressions? Check out this video for a step-by-step guide and clear explanation!
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🔥 Keywords limit, tangent, sine, cosine, algebraic manipulation, expression, equivalent expressions, simplify, pi/4, unit circle, root, negative, step by step, math.
🔥 Common misspellings limmit, tangant, sin, cosin, algebric, expresion, simplfy, pi/4th, rooot, negetive, step-by-step, maths.
🔥 Tags #limit #algebra #mathematics #tangent #sine #cosine #expression #equivalentexpressions #simplify #pi/4 #unitcircle #root #negative #stepbystep #math.
🔥 7 Common Internet Questions
1️⃣ What is the limit of (1 - tan x) / (sin x - cos x) as x approaches pi/4?
The answer is -√2.
2️⃣ How do you simplify the expression (1 - tan x) / (sin x - cos x)?
We use algebraic manipulation to rewrite the expression and simplify it.
3️⃣ What is the identity for tangent?
Tangent can be expressed as sine over cosine.
4️⃣ What are equivalent expressions for cosine x minus sine x?
Sine x minus cosine x.
5️⃣ What is the unit circle?
A circle with a radius of 1, used to understand the values of sine and cosine for different angles.
6️⃣ How do you find the value of cosine pi/4?
The value of cosine pi/4 is √2 / 2.
7️⃣ How do you find the limit of a function?
You can find the limit of a function using algebraic manipulation, substitution, or other methods.