# prove that: sin (2 x 30°) = 2 tan 30 ° 1 + tan 2 30 ° - Mathematics

Sum

prove that:

sin (2 x 30°) = (2 tan 30°)/(1+tan^2 30°)

#### Solution

RHS = (2 tan 30°)/(1+tan^2 30°) = (2xx1/(sqrt3))/(1 +(1/sqrt3)^2) = (2/(sqrt3))/(1+(1)/(3)) = (2/sqrt3)/(4/(3)) = (sqrt3)/(2)

LHS = sin (2 x 30°) = sin 60° = (sqrt3)/(2)

∴ LHS = RHS

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 (A) | Q 4.1 | Page 291