Question

Prove that cosh ²x - sinh2x = 1.​

Answer 1

Answer:

$cos {}^{2} x - sinh2x = 1$

$cos {}^{2} x - sinh {}^{2} x = (\frac{e {}^{x} + e { }^{ - x} }{2} ) {}^{2} - ( \frac{e {}^{x} - e {}^{ - x} }{2} ) {}^{2}$

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

$= \frac{4}{4}$

$= 1.$

is your right answer