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Choose the correct answer in each of the following questions: `(cos0^(@)+sin30^(@) +sin45^(@))(sin 90^(@) + cos60^(@)-cos45^(@))=?`

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Choose the correct answer in each of the following questions:
`(cos0^(@)+sin30^(@) +sin45^(@))(sin 90^(@) + cos60^(@)-cos45^(@))=?`
A. `(5)/(6)`
B. `(5)/(8)`
C. `(3)/(5)`
D. `(7)/(4)`
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1 Answer

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Correct Answer - D
`(cos0^(@)sin30^(@)+sin45^(@))(sin90^(@)+cos60^(@)-cos45^(@))`
`=(1+(1)/(2)+(1)/(sqrt(2)))(1+(1)/(2)-(1)/(sqrt(2)))=((3)/(2)+(1)/(sqrt(2)))((3)/(2)-(1)/(sqrt(2)))=((9)/(4)-(1)/(2))=(7)/(4).`
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