s∈²θ + cos²θ = 1
tanθ = s∈θ/cosθ
cosecθ = 1/s∈θ
secθ = 1/cosθ
cotθ = cosθ/s∈θ
s∈(α + β) = s∈αcosβ + cosαs∈β
cos(α + β) = cosαcosβ - s∈αs∈β
s∈(α - β) = s∈αcosβ - cosαs∈β
cos(α - β) = cosαcosβ + s∈αs∈β
s∈²θ = (1 - cost)/2
cos²θ = (1 + cost)/2
eⁱᵞ = cosθ + i s∈θ
∑ₙ₌₁ⁿ aₙ = n(a₁ + aₙ)/2
∑ₙ₌₁ⁿ aₙ = n(a₁ + aₙ)/2 for AP
∑ₙ₌₁ⁿ aₙ = a₁ * (rⁿ - 1)/(r - 1) for GP
ⁿCᵣ = n!/(r!(n-r)!)
P(ⁿCᵣ * pᵣ * qⁿ⁻ᵣ) = (ⁿCᵣ * pᵣ * qⁿ⁻ᵣ)
E = mc²
F = GmM/r²
v = u + at
d/dx (xⁿ) = nxⁿ⁻¹
limₓ→₀ (s∈ x)/x = 1
PV = nRT
λ = h/(mv)

🪤 The 5 Mistakes That Cost Marks

Not checking the units of the answer
Forgetting to consider all possible cases
Not using the correct formula
Making calculation errors
Not reading the question carefully

✏️ 3 Solved PYQs

Question 1: Find the value of ∫(x² + 1)/x dx
- Let's assume I = ∫(x² + 1)/x dx
- I = ∫(x + 1/x) dx
- I = ∫x dx + ∫1/x dx
- I = x²/2 + log|x| + C
Question 2: Find the equation of the tangent to the curve y = x³ - 2x² + x + 1 at x = 1
- dy/dx = 3x² - 4x + 1
- dy/dx at x = 1 is 3(1)² - 4(1) + 1 = 0
- The equation of the tangent is y - 1 = 0(x - 1)
- y = 0
Question 3: Find the value of s∈(π/4 + π/6)
- s∈(π/4 + π/6) = s∈(π/4)cos(π/6) + cos(π/4)s∈(π/6)
- s∈(π/4 + π/6) = (1/√2)(√3/2) + (1/√2)(1/2)
- s∈(π/4 + π/6) = (√3 + 1)/(2√2)

🧠 The One Thing Most Students Get Wrong

Most students get wrong the concept of limits and continuity
They often confuse the two concepts and are unable to apply them correctly
Limits are used to study the behavior of a function as the input gets arbitrarily close to a certa∈ point
Continuity is used to study the behavior of a function at a certa∈ point
A function can have a limit at a point but not be continuous at that point

👁️ Ayush's Note

Always try to simplify the expression before solving the problem
Use the correct formula and units
Check the answer for any calculation errors
Consider all possible cases
Use the concept of limits and continuity correctly
Practice as many problems as possible to get a good grasp of the concepts
For JEE Advanced and NEET level problems, use shortcuts like
- Using the formula for the sum of a geometric progression to solve problems related to sequences and series
- Using the formula for the derivative of a function to solve problems related to maxima and minima
- Using the formula for the integral of a function to solve problems related to area under curves

🔁 Last 5 Minutes Box

Check the units of the answer
Check for any calculation errors
Consider all possible cases
Use the correct formula
Read the question carefully
For JEE Advanced and NEET level problems, use shortcuts like
- Using the formula for the sum of a geometric progression to solve problems related to sequences and series
- Using the formula for the derivative of a function to solve problems related to maxima and minima
- Using the formula for the integral of a function to solve problems related to area under curves

📝 Practice MCQs

1. What is the value of s∈(π/4 + π/6)?

A) (√3 - 1)/(2√2)

B) (√3 + 1)/(2√2)

C) (√2 + 1)/(2√3)

D) (√2 - 1)/(2√3)

Answer: B) (√3 + 1)/(2√2)

2. What is the equation of the tangent to the curve y = x³ - 2x² + x + 1 at x = 1?

A) y = x - 1

B) y = x + 1

C) y = 0

D) y = 2x - 1

Answer: C) y = 0

3. What is the value of ∫(x² + 1)/x dx?

A) x²/2 + log|x| + C

B) x²/2 - log|x| + C

C) x²/2 + log|x| - C

D) x²/2 - log|x| - C

Answer: A) x²/2 + log|x| + C

4. What is the value of limₓ→₀ (s∈ x)/x?

A) 0

B) 1

C) ∞

D) -1

Answer: B) 1

5. What is the value of ∑ₙ₌₁ⁿ aₙ for an arithmetic progression?

A) n(a₁ + aₙ)/2

B) n(a₁ - aₙ)/2

C) n(a₁ * aₙ)/2

D) n(a₁ + aₙ)

Answer: A) n(a₁ + aₙ)/2

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📚 Academic References

Content verified against peer-reviewed research:

When do people rely on algorithms — eScholarship (California Digital Library) (2016) 🔓 — DOI ↗
Hippocratic Oaths for Mathematicians? — Philosophia (2022) 🔓 — DOI ↗
The Phenomenon of Abstract Cognition Among Scholastic Chess Parti... — Digital Commons - East Tennessee State University (East Tennessee State University) (2014) 🔓 — DOI ↗

🔓 = Open Access article

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This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides:

s∈²θ + cos²θ = 1
tanθ = s∈θ/cosθ
cosecθ = 1/s∈θ
secθ = 1/cosθ
cotθ = cosθ/s∈θ
s∈(α + β) = s∈αcosβ + cosαs∈β
cos(α + β) = cosαcosβ - s∈αs∈β
s∈(α - β) = s∈αcosβ - cosαs∈β
cos(α - β) = cosαcosβ + s∈αs∈β
s∈²θ = (1 - cost)/2
cos²θ = (1 + cost)/2
eⁱᵞ = cosθ + i s∈θ
∑ₙ₌₁ⁿ aₙ = n(a₁ + aₙ)/2
∑ₙ₌₁ⁿ aₙ = n(a₁ + aₙ)/2 for AP
∑ₙ₌₁ⁿ aₙ = a₁ * (rⁿ - 1)/(r - 1) for GP
ⁿCᵣ = n!/(r!(n-r)!)
P(ⁿCᵣ * pᵣ * qⁿ⁻ᵣ) = (ⁿCᵣ * pᵣ * qⁿ⁻ᵣ)
E = mc²
F = GmM/r²
v = u + at
d/dx (xⁿ) = nxⁿ⁻¹
limₓ→₀ (s∈ x)/x = 1
PV = nRT
λ = h/(mv)