Question

10. Prove that tan 15° = 2 -√ 3​

Answer 1

To Prove:-

15° = 2 -√ 3

Step By Step Explanation:-

tan( A - B ) = (tan A -tan B) / (1 + tanA × tan B)

→ Let A =45

→ B=30

we know that,

tan 45° = 1

tan 30° = 1/√3

LHS = tan 15°

RHS = (tan 45° -tan 30°) / (1+tan45° ×tan 30°)

=> (1- 1/√3)/ (1 +1√3)

=>(√3-1)/(√3+1)

=> (√3-1)²/ (√3+1) × (√3-1)

=> (3+1-2√3) / (3-1)

=> (4-2√3) / 2

=> 2-√3

°•° Hence proved