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 23 Evaluate $\cos 18^\circ$ without using the calculator 18 Intro to Real Analysis 16 Prove by contradiction that a real number that is less than every positive real number cannot be posisitve 12 Integral $-\int_{0}^{a}{at^{3}\,{\rm d}t\over\,\sqrt{\,\left(a^{2} -t^{2}\right)\left(b^{2}t^{2} +a^{4}-a^{2}t^{2}\right)\,}\,}$ 8 Finding $\frac{a+b}{a-b}$ such that $a^2+b^2=6ab$

### Reputation (4,444)

 +30 Evaluate $\cos 18^\circ$ without using the calculator +10 Logarithm proof problem: $a^{\log_b c} = c^{\log_b a}$ +10 Is this correct method to prove that $a^2 + b^2 + c^2 ≥ ab + bc + ac$, when $a,b,c \geq 0$? +10 Qns on Propositional Logic - Inference Rules + Logical Equivalence

### Questions (17)

 16 What is $i$ exponentiated to itself $i$ times? 7 How did Euler solve the 4-whole-numbers-adding-up-to-a-perfect-square problem? 6 Solve $\operatorname{Arg} (z-2) - \operatorname{Arg} (z+2) = \frac{\pi}{6}$ 6 Prove $(A \triangle B) \cap (B\triangle C) \cap (C\triangle A) = \emptyset$ 5 If $a+b=x$ and $ab=y$, what is the quickest way to solve for $a$ and $b$?

### Tags (73)

 65 trigonometry × 24 22 integration × 8 48 algebra-precalculus × 27 22 inequality × 7 39 calculus × 27 16 logic × 11 26 elementary-set-theory × 17 16 reference-request 24 real-analysis × 8 16 self-learning

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