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Question
Find the value of the following:
(sin 90° + cos 60° + cos 45°) × (sin 30° + cos 0° – cos 45°)
Solution
sin 90° = 1, cos 60° = `1/2`, cos 45° = `1/sqrt(2)`, sin 30° = `1/2`, cos 0° = 1
(sin 90° + cos 60° + cos 45°) × (sin 30° + cos 0° – cos 45°)
= `(1 + 1/2 + 1/sqrt(2)) xx (1/1 + 1 - 1/sqrt(2))`
= `((2sqrt(2) + sqrt(2) + 2)/(2sqrt(2))) xx ((sqrt(2) + 2sqrt(2) - 2)/(2sqrt(2)))`
= `((3sqrt(2) + 2)/(2sqrt(2))) xx ((3sqrt(2) - 2)/(2sqrt(2)))`
= `((3sqrt(2))^2 - (2)^2)/8`
= `(9(2) - 4)/8`
= `(18 - 4)/8`
= `14/8`
= `7/4`
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