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Question
Evaluate the following:
(cos 0° + sin 45° + sin 30°)(sin 90° – cos 45° + cos 60°)
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Solution
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°) ....(i)
By trigonometric ratios we have
`cos 0^@ = 1, sin 45^@ = 1/sqrt2, sin 30^@ = 1/2, sin 90^@ = 1, cos 45^@ = 1/sqrt2 cos 6062 = 1/2`
By substituting above values in (i), we get
`(1 + 1/sqrt2 + 1/2)(1 - 1/sqrt2 + 1/2)`
`[3/2 + 1/sqrt2 + 1/sqrt2] [3/2 - 1/sqrt2] => [3/2]^2 - [1/sqrt2]= 9/4 - 1/2 = 7/4`
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