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We need to evaluate the expression: $\frac{sin(\frac{2\pi}{3}) + cos(\frac{\pi}{4})}{tan(\frac{\pi}{...
TrigonometryTrigonometric FunctionsExpression EvaluationRadians
2025/5/22
The image presents a math exam with several problems related to complex numbers, limits, integrals, ...
Complex NumbersLimitsIntegralsDifferential Equations3D GeometryAlgebraTrigonometry
2025/5/11
The problem has three parts: (i) Differentiate $y = 2x^3 \sin 2x$ with respect to $x$. (ii) Simplify...
DifferentiationProduct RuleExponentsComplex NumbersSimplificationComplex Conjugate
2025/5/8
We are given three problems: a) Given two sets $M$ and $N$, find their union and intersection. $M$ i...
Set TheoryArithmeticGeometryOrder of OperationsAnglesStraight LinesRatio and Proportion
2025/4/29
We are asked to prove the trigonometric identity: $1 - 2\cos^2{t} = \frac{\tan^2{t} - 1}{\tan^2{t} +...
TrigonometryTrigonometric IdentitiesProofs
2025/4/28
The problem is to simplify the expression $\sin^2{\alpha} + \sin{\alpha}\cos^2{\alpha}$.
TrigonometryTrigonometric IdentitiesExpression Simplification
2025/4/25
The problem defines a function $G$ that takes a student's first name as input and returns the number...
FunctionsString ManipulationCounting
2025/4/24
The problem asks to name the given organic compounds (alkanes) based on their structures and write o...
Organic ChemistryIsomersNomenclatureAlkanesStructural Formulas
2025/4/21
The problem description would clearly state what needs to be calculated or proven. For example: "Sol...
Mathematical FormulasUnspecified ProblemImage Analysis
2025/4/10
The image contains three questions. Let's address the questions one by one. Question 1: What is the ...
Computer ScienceInteger RepresentationComparison Operations
2025/4/4