prove that: tan (2 x 30°) = 2 tan 30 ° 1 – tan 2 30 ° - Mathematics

Sum

prove that:

tan (2 x 30°) = (2 tan 30°)/(1– tan^2 30°)

Solution

RHS,

(2 tan^2 30°)/(1 – tan^2 30°) = (2 (1)/sqrt3)/(1– 1/3) = (2/sqrt3)/(2/3) = sqrt3

LHS,
tan (2 x 30°) = tan 60° = sqrt3
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 4.3 | Page 291