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If A = 30°; show that: cos 3 A – cos 3 A cos A + sin 3 A + sin 3 A sin A = 3 - Mathematics

Sum

If A = 30°;
show that:
`(cos^3"A" – cos 3"A")/(cos "A") + (sin^3"A" + sin3"A")/(sin"A") = 3`

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Solution

Given that A = 30°

LHS = `(cos^3 "A" – cos 3"A")/(cos "A") + (sin^3 "A" + sin 3"A")/(sin "A")`

= `(cos^3 30° – cos3 (30°))/(cos 30°) + (sin^3 30° + sin3 (30°))/(sin 30°)`

= `((sqrt3/2)^3 – 0)/(sqrt3/2) + ((1/2)^3 + 1)/(1/2)`

= `(sqrt3/2)^2 + (9/8)/(1/2)`

= `(3)/(4) + (9)/(4)`

= `(12)/(4)`

= 3

= RHS

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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 4.7 | Page 293
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