As you know there are these trigonometric formulas like Sin 2x, Cos 2x, Tan 2x which are known as double angle formulae for they have double angles in them. To get a good understanding of this topic, Let’s go through the practice examples provided.
Bạn đang xem: Cos2x
Introduction to Cos 2 Theta formulaLet’s have a look at trigonometric formulae known as the double angle formulae. They are said to be so as it involves double angles trigonometric functions, i.e. Cos 2x.
Deriving Double Angle Formulae for Cos 2t
Let’s start by considering the addition formula.
Cos(A + B) = Cos A cos B – Sin A sin B
Let’s equate B to A, i.e A = B
And then, the first of these formulae becomes: Cos(t + t) = Cos t cos t – Sin t sin t
so that Cos 2t = Cos2t – Sin2t
And this is how we get second double-angle formula, which is so called because you are doubling the angle (as in 2A).
Xem thêm: Quán Quân Olympia 2021 - Quán Quân Olympia 21: Ước Mơ Trở Thành Doanh Nhân
Practice Example for Cos 2:
Solve the equation cos 2a = sin a, for – Π
It becomes 1 − 2 sin2 a = sin a
2 sin2 a + sin a − 1=0,
Let’s factorise this quadratic equation with variable sinx
(2 sin a − 1)(sin a + 1) = 0
2 sin a − 1 = 0 or sin a + 1 = 0
sin a = 1/2 or sin a = −1
To check other mathematical formulas and examples, visit BYJU’S.
|FORMULAS Related Links|
|Maths Important Formulas Pdf||Combined Mean Formula|
|All Physics Formulas And Equations||Formula Of Cone And Sphere|
|Farenheit To Celcius Formula||Margin Of Error Formula|
|Maths Formulas For Class 5||Lateral Surface Area Of A Cone|
|Dimensional Formula Of Kinetic Energy||Heat Gain Formula|
Leave a Comment Cancel reply
Your Mobile number and Email id will not be published. Required fields are marked *
Join BYJU'S Learning Program
Grade/ExamClass 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12IASCATBank ExamGATE
FREE TEXTBOOK SOLUTIONS
×Book a Free Class
GradeClass 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12IASCATBank Exam