Sum

If A = 30°; **show that:**

`(1 + sin 2"A" + cos 2"A")/(sin "A" + cos"A") = 2 cos "A"`

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#### 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`

Concept: Trigonometric Ratios of Some Special Angles

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