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Question
Evaluate :
`(3 sin 3"B" + 2 cos(2"B" + 5°))/(2 cos 3"B" – sin (2"B" – 10°)` ; when "B" = 20°.
Solution
Given that B = 20°
`(3 sin 3"B"+2 cos(2"B"+5°))/(2 cos 3"B" – sin (2"B" – 10°)` = `(3 sin 3 xx 20°+2 cos(2 xx 20°+5°))/(2 cos 3 xx 20° – sin (2 xx 20° – 10°))`
= `( 3 sin 60° + 2 cos 45°)/(2 cos 60° – sin 30°)`
= `(3(sqrt3/2) + 2(1/sqrt2))/(2(1/2) – (1)/(2)`
= `(3(sqrt3)/(2) + sqrt2)/(2)`
= `3 sqrt3 + 2 sqrt2`
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