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Find the value of ((cos1^(@)+sin1^(@))(c...

Find the value of `((cos1^(@)+sin1^(@))(cos2^(@)+sin2^(@))(cos3^(@)+sin3^(@))...(cos 45^@sin45^@))/( cos1^(@)cos2^(@)cos3^(@)...cos45^(@)) `

Text Solution

Verified by Experts

The correct Answer is:
`2^(23)`
Multiplying and dividing each factor of numerator with `sqrt(2)`, we get
`E=(sqrt(2)sin(45^(@)+1^(@))sqrt(2)sin(45^(@)+2^(@)).......(sqrt(2)sin(45^(@)+45^(@))))/(cos1^(@)cos2^(@)cos3^(@)........cos45^(@))`
`=(sqrt(2))^(45)((sin46^(@))/(cos44^(@)))((sin47^(@))/(cos53^(@)))((sin48^(@))/(cos42^(@)))-((sin89^(@))/(cos1^(@)))((sin90^(@))/(cos 45^(@)))`
`=2^(23)`
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