Question

show that cosiy=coshy​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

cos iy = coshy is proved

Given : cos iy = coshy

To find : To prove

Solution :

Step 1 of 2 :

Write down the equation to prove

The given equation is

cos iy = coshy

Step 2 of 2 :

Prove the equation

We know that

$\displaystyle \sf{ cosx = \frac{ {e}^{ix} + {e}^{ - ix} }{2} }$

Putting x = iy we get

$\displaystyle \sf{ cos iy = \frac{ {e}^{i.iy} + {e}^{ - i.iy} }{2} }$

$\displaystyle \sf{ \implies \: cos iy = \frac{ {e}^{ {i}^{2} y} + {e}^{ - {i}^{2} y} }{2} }$

$\displaystyle \sf{ \implies \: cos \: iy = \frac{ {e}^{ - y} + {e}^{ y} }{2} }$

$\displaystyle \sf{ \implies \: cos \: iy = \frac{ {e}^{y} + {e}^{ - y} }{2} }$

$\displaystyle \sf{ \implies \: cos \: iy = coshy }$

Hence proved

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