(√3 + 1) (3 - cot 30°) = tan³ 60° - 2 sin 60°. Prove the following statement

Solution:

LHS = (√3 + 1) (3 - cot 30°)

We know that cot 30° = √3

= (√3 + 1) (3 - √3)

We can write (3 - √3) = √3 (√3 - 1)

= (√3 + 1) √3 (√3 - 1)

Using the algebraic identity (√3 + 1)(√3 - 1) = ((√3)² - 1)]

= ((√3)² - 1) √3

= (3 - 1) √3

= 2√3

Let us solve RHS = tan³ 60° - 2 sin 60°

Since, tan 60⁰ = √3 and sin 60⁰ = √3/2,

We get,

(√3)³ - 2.(√3/2) = 3√3 - √3

= 2√3

Therefore, it is proved that LHS = RHS.

✦ Try This: Evaluate 3 sin 60° - 4 sin³ 60°

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

NCERT Exemplar Class 10 Maths Exercise 8.3 Problem 5

(√3 + 1) (3 - cot 30°) = tan³ 60° - 2 sin 60°. Prove the following statement

Summary:

It is proved that (√3 + 1) (3 - cot 30°) = tan³ 60° - 2 sin 60°

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