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If A = 30°; show that: 1 + sin 2 A + cos 2 A sin A + cos A = 2 cos A - Mathematics

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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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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Exercise 23 (B) | Q 4.5 | Page 293
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