2 ways: trig Show tan(2x)=2/(cot(x)-tan(x))

Early iconic scene of Korean “Old Demon” Yin Wangchan

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trig Write each expression as an equivalent algebraic expression involving only x.

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2 ways: sq root derivative 1/(√√(1/√x))

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example: Mean, Median & Mode

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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🪔 Happy Deepavali 🪔 [Nov-12-2023]

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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This can’t be blamed on Han Li.

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4th/5ways: triangular num: Show t(n-1) + tn = n^2 where tn = nth triangular number

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Review: Product to Sum Identities

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Bijection of elements in tn & a pair of elements of (n+1)

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Review Add Math: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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Show Σ(a+bk) = (a+1/2bn)(n+1)

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Growing patterns #2

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#5 MIT 2022 Integration Bee Qualifying Exam

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trig integral ∫1/(√sin(x) √cos^7(x)) dx

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3 ways: derivative log(x+ (1+√(x^2)))

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Polite number

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The University of Maine: rational function integral compute

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