Prove that cosh² x- sinh²x=1Pa help po please @Robbespier.Paki skip na lmg po if...

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SilentKnight08 @SilentKnight08

October 2022 1 2 Report

Prove that cosh² x- sinh²x=1

Pa help po please @Robbespier.

Paki skip na lmg po if dimo alam

Answers & Comments

Robbespierre

PROOFS:

$\small \sf{sinh = \frac{e {}^{x} - e {}^{ - x} }{2} }$

$\small \sf{coshx = \frac{e {}^{x} + e {}^{ - x} }{2} }$

So we have:

$\small \rm{cosh {}^{2} x - sinh {}^{2}x = ( \frac{ e {}^{x} + e {}^{ - x} }{2} ) {}^{2} - ( \frac{e {}^{x} - e {}^{ - x} }{2} ) {}^{2} }$

$= \frac{e {}^{2x} + 2e {}^{x} e {}^{ - x} + e {}^{ - 2x} }{4} - \frac{e {}^{2x} - 2e {}^{2x} e {}^{ - x} + e {}^{ - 2x} }{4}$

$= \frac{e {}^{2x} + 2 + e {}^{ - 2x} + 2 - e {}^{ - 2x} }{4}$

$= \frac{2 + 2}{4}$

$\sf \underline \red{ = 1}$

#CarryOnLearning

Robbespierre Do i need to?

SilentKnight08 Waw english. Nosebleed ako haha

SilentKnight08 Ano na kuya/ate ikw po ba un? oo o hindi lng eh

SilentKnight08 Oo o hindi lang nmn eh.

SilentKnight08 Pag dimo sinagut kuya/ate. Help mo na lang ako ulet x'D hihi

SilentKnight08 HAHA di nm eh

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PROOFS:

So we have:

#CarryOnLearning

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