![Ex 3.3, 5 - Find the value of tan 15° [with Video] - Trigonometry - Ex 3.3](https://cdn.teachoo.com/ee185f5b-d081-4d2a-b732-d539b30c8890/slide12.jpg)
Ex 3.3, 5 (ii) - Chapter 3 Class 11 Trigonometric Functions
Last updated at Dec. 16, 2024 by Teachoo
Ex 3.3
Ex 3.3, 1
Important
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Chapter 3 Class 11 Trigonometric Functions
Serial order wise
Transcript
Ex 3.3, 5 Find the value of: (ii) tan 15° tan 15° = tan (45° – 30°) = (tan 45° − 〖 tan〗〖30°〗)/(1 + tan 45°tan〖30°〗 ) = (1 − 1/√3)/(1 + 1 × 1/√3) = ((√3 − 1" " )/√3)/((√3 + 1" " )/√3) = (√3 −1)/√3 × √3/(√3 + 1) = (√𝟑 − 𝟏)/(√𝟑 + 𝟏) Rationalizing = (√3 − 1)/(√3 + 1) × (√3 − 1)/(√3 − 1) = (√3 − 1)2/(√3 + 1)(√3 − 1) Using (a – b)2 = a2 + b2 – 2ab = ((√3)2 + 12 − 2" " × √3 × 1)/(√3 + 1)(√3 − 1) = (3 + 1 − 2√3)/(√(3 )+ 1)(√3 − 1) Using (a – b ) (a + b) = a2 – b2 = (𝟒 − 𝟐√𝟑)/((√𝟑)𝟐 − (𝟏)𝟐) = (4 − 2√3)/(3 − 1) = (2 (2 − √(3 )))/2 = 2 – √𝟑 Hence, tan 15° = 2 – √𝟑
