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Question
If A = 30°;
show that:
`(1 + sin 2"A" + cos 2"A")/(sin "A" + cos"A") = 2 cos "A"`
Solution
Given that A = 30°
LHS = `(1 + sin2"A" + cos2"A")/(sin "A" + cos "A")`
= `(1 + sin2 (30°) + cos2 (30°))/(sin 30° + cos 30°)`
= `(1 +(sqrt3)/(2) + (1)/(2))/((1)/(2) + (sqrt3)/(2)`
= `(3 + sqrt3)/(sqrt3 + 1)((sqrt3 – 1)/(sqrt3– 1))`
= `(3 sqrt3 – 3 + 3 – sqrt3)/(2)`
= `2 (sqrt3)/(2)`
= `sqrt3`
RHS = 2 cos A
= 2 cos (30°)
= `2(sqrt3/2)`
= `sqrt3`
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