We will learn step-by-step the proof of cotangent formula cot (α - β).
Prove that, cot (α - β) = cot α cot β + 1/cot β - cot α.
Proof: cot (α - β) = cos(α - β)/sin (α - β)
= cos α cos β + sin α sin β/sin α cos β - cos α sin β
= cos α cos β/sin α sin β + sin α sin β/sin α sin β/sin α cos β/sin α sin β - cos α sin β/sin α sin β, [dividing numerator and denominator by sin α sin β].
= cot α cot β + 1/cot β - cot α Proved
Therefore, cot (α - β) = cot α cot β + 1/cot β - cot α.
Solved
examples using the proof of cotangent formula cot (α - β):
1. Find the value of cot 15°.
Solution:
cot 15°
= cot (45° - 30°)
= cot 45° cot 30° + 1/cot 30° - cot 45°
= 1 ∙ √3 + 1/√3 - 1
= √3 + 1/√3 - 1
= (√3 + 1)^2/(√3 - 1) (√3 + 1)
= 3 + 2√3 + 1/3 – 1
= 4 + 2√3/2
= 2 + √3
11 and 12 Grade Math
From Proof of Proof of Cotangent Formula cot (α - β) to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Apr 20, 24 05:39 PM
Apr 20, 24 05:29 PM
Apr 19, 24 04:01 PM
Apr 19, 24 01:50 PM
Apr 19, 24 01:22 PM