Prove that:

\({ \left( { e }^{ \sqrt { { e }^{ \ln { \left( \frac { { 3 }^{ 0 } }{ \sin { \left( \frac { \pi }{ 2 } \right) } } \right) } } } } \right) }^{ \ln { \left( \sqrt { { e }^{ \ln { \left( \frac { { 3 }^{ 0 } }{ \sin { \left( \frac { \pi }{ 2 } \right) } } \right) } } } \right) } }=1\)

Show your workings.

Question

21-02-2015
Mathematics

Answered

Prove that:

\({ \left( { e }^{ \sqrt { { e }^{ \ln { \left( \frac { { 3 }^{ 0 } }{ \sin { \left( \frac { \pi }{ 2 } \right) } } \right) } } } } \right) }^{ \ln { \left( \sqrt { { e }^{ \ln { \left( \frac { { 3 }^{ 0 } }{ \sin { \left( \frac { \pi }{ 2 } \right) } } \right) } } } \right) } }=1\)

Show your workings.

Verified Answer :

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konrad509 konrad509 · Answer 1 · 2015-02-21T16:51:04-05:00

\({ \left( { e }^{ \sqrt { { e }^{ \ln { \left( \frac { { 3 }^{ 0 } }{ \sin { \left( \frac { \pi }{ 2 } \right) } } \right) } } } } \right) }^{ \ln { \left( \sqrt { { e }^{ \ln { \left( \frac { { 3 }^{ 0 } }{ \sin { \left( \frac { \pi }{ 2 } \right) } } \right) } } } \right) } }=1\\ { \left( { e }^{ \sqrt { { e }^{ \ln { \left( \frac { 1 }{ 1} \right) } } } } \right) }^{ \ln { \left( \sqrt { { e }^{ \ln { \left( \frac { 1 }{1 } \right) } } } \right) } }=1\\\)
\({ \left( { e }^{ \sqrt { { e }^{ \ln 1 } } } \right) }^{ \ln { \left( \sqrt { { e }^{ \ln 1 } } \right) } }=1\\ { \left( { e }^{ \sqrt 1 } \right) }^{ \ln { \left( \sqrt 1 \right) } }=1\\ { \left( { e }^ 1 \right) }^{ \ln 1 }=1\\ e ^{ \ln 1 }=1\\1=1\)