# Prove that: ( tan 60 ° + 1 tan 60 ° – 1 ) 2 = 1 + cos 30 ° 1 – cos 30 ° - Mathematics

Sum

Prove that:

((tan60°  + 1)/(tan 60°  – 1))^2 = (1+ cos 30°) /(1– cos 30°)

#### Solution

LHS = ((tan60°+ 1)/(tan 60° – 1))^2

= ((sqrt3 +1)/(sqrt3 – 1))^2 = (4 + 2sqrt3)/(4–2sqrt3 ) = (1+sqrt3/2)/(1– sqrt3/2) = (1+ cos 30°) /(1– cos 30°) = RHS

Concept: Trigonometric Ratios of Some Special Angles
Is there an error in this question or solution?

#### 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 3.5 | Page 291