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Trigonometric and Hyperbolic Identities, Thesis of Mathematics

Dr. A.P.J. Abdul Kalam Technical UniversityMathematics

A list of trigonometric and hyperbolic identities, including derivatives and rules. It covers topics such as product rule, quotient rule, and sum and difference formulas. The document also includes identities for double and triple angles, as well as inverse trigonometric functions. The identities are useful for solving equations and simplifying expressions in calculus and trigonometry.

Typology: Thesis

2022/2023

Available from 12/02/2023

aditya-mishra-20
aditya-mishra-20 🇮🇳

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STANDARD RESULTS 1. 4 act) = nxt d . = (e) =e 3. ae (e*) d 1 5. ae (logy x) = Si logy, @ 7. ©£ (cos x) =-sinx dx 9. ies (cosec x) = — cosec x cot x dx a af (see x) = sec x tan x dx d F Ie 13. 7 (cost x) = ae d 1 16. "sec"! x) = ———= dx x x7 -1 rf d ze 17. © (cosec* x) =- —==—— dx xy x? 1 ey ook \ h =. e+e 19. cosh x a 2: 4 (a*) = a* log, a d 22 4.7 (log, #) = = 6. aaa (sin x) = cos x dx g. 4 (tan x) = sec? x dx 10. 4 (cot x) = — cosec? « dx dives & 1 12, = (sin x) = ne 14. < (tan x) = —z ix d 1x) = 16. a (cot * x) = eee x _ ook 18. sinh x = © zs Ba es 20. tanh « = eit 21. cosh? x — sinh? x = 1, sech? x + tanh? x = 1, coth? x = 1 + cosech? x 22. cosh? x + sinh? x = cosh 2x 23. sinh x = log (x + yx” +1), cosh”*« = log (x + x? -1) 24, 4 (sinh x) = cosh x dx 26. & (tanh x) = sech? x dx d 28. ae (sech x) =— sech x tanh x d dv du 30. Product —— Su ape ct rule: (wv) =u— +0 dy _dy dt. 32. Ge ape ify = f,(@) and x =f,(¢) (xiii) gl (cosh x) = sinh x dx 25. 27. < (coth x) = — cosech? x al d 29. Fs (cosech x) = — cosech x cothx ; d (u 81. Quotient rule: ms (| b$] CamScanner