If x/a cos theta + y/b sin theta 1
WebSolution. The correct option is A. ( b tan θ) / a. Step 1: Simplify x = a sin 2 θ ( 1 + cos 2 θ). We know that sin 2 θ = 2 sin θ cos θ. ⇒ cos 2 θ = 2 cos 2 θ – 1 ⇒ x = 2 a sin θ cos θ ( 1 + 2 cos 2 θ - 1) = 2 a sin θ cos θ × 2 cos 2 θ = 4 a sin θ cos 3 θ. Step 2: Differentiate x w.r.t. θ. d x / d θ = 4 a ( cos θ × cos ... WebIf x = a (cos θ + θ sin θ) and y = a (sin θ − θ cos θ) where 0 < θ < 2 π , then d x 2 d 2 y at θ = 4 π is equal to 4816 75 COMEDK COMEDK 2010 Continuity and Differentiability Report Error
If x/a cos theta + y/b sin theta 1
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WebIf a sin θ+b cos θ= c, then prove that a cos θ−b sin θ= √a2+b2−c2 Solution Given that, a sin θ+b cos θ =c On squaring both sides, (a sin θ+b cos θ)2 =c2 ⇒ a2 sin2 θ+b2 cos2 θ+2ab sin θ.cos θ=c2 [∵(x+y)2 =x2+2xy+y2] ⇒ a2(1−cos2 θ)+b2(1−sin2 θ)+2ab sin θ.cos θ =c2 [∵sin2 θ+cos2 θ=1] ⇒ a2−a2 cos2 θ+b2−b2 sin2 θ+2ab sin θ.cos θ= c2 Web29 mrt. 2024 · Transcript. Question 3 If sin𝜃 = x and sin𝜃 = y , then tan𝜃 is (a) 𝑥𝑦 (b) 𝑥/𝑦 (c) 𝑦/𝑥 (d) 1/𝑥𝑦 Given 𝒔𝒊𝒏𝜽 = x And, sec𝜃 = y 1/cosθ = y 𝒄𝒐𝒔𝜽 = 1/𝑦 Now, 𝒕𝒂𝒏𝜽=sinθ/cosθ = 𝑥/ (1/𝑦) = 𝒙𝒚 So, the correct answer is (a) Next: Question ...
Web30 mrt. 2024 · Example 34 Find 𝑑𝑦/𝑑𝑥 , if 𝑥 = 𝑎 cos𝜃, 𝑦 = 𝑎 sin θ.Here 𝑑𝑦/𝑑𝑥 = (𝑑𝑦/𝑑𝜃)/ (𝑑𝑥/𝑑𝜃) Calculating 𝒅𝒚/𝒅𝜽 𝑦 = 𝑎 sin θ 𝑑𝑦/𝑑𝜃 = 𝑑 (𝑎 sin 𝜃)/𝑑𝜃 𝑑𝑦/𝑑𝜃 = 𝒂 𝒄𝒐𝒔𝜽 Calculating 𝒅𝒙/𝒅𝜽 𝑦 = 𝑎 cos θ ... WebJacobian matrix and determinant. In vector calculus, the Jacobian matrix ( / dʒəˈkoʊbiən /, [1] [2] [3] / dʒɪ -, jɪ -/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the ...
WebIf x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that y2 (d2y)/(dx2)-xdy/dx+y=0 . CBSE Commerce (English Medium) Class 12. Question Papers 1852. Textbook Solutions 19127. MCQ Online Mock Tests 29. Important Solutions 4688. Question Bank Solutions 24139. Concept Notes & Videos 242. WebProve that : `x cos theta + y sin theta = a and x sin theta - y cos theta = b` are the parametric equations of a circle for all `theta` satisfying `0le theta...
Web30 mrt. 2024 · Ex 5.6, 6 If x and y are connected parametrically by the equations without eliminating the parameter, Find 𝑑𝑦/𝑑𝑥, 𝑥 = 𝑎 (𝜃 – sin𝜃), 𝑦 = 𝑎 (1 + cos𝜃)Here 𝑑𝑦/𝑑𝑥 = (𝑑𝑦/𝑑𝜃)/ (𝑑𝑥/𝑑𝜃) Calculating 𝒅𝒚/𝒅𝜽 𝑦 = 𝑎 (1+cos𝜃) 𝑑𝑦/𝑑𝜃 ...
Web26 jul. 2024 · If `x = a cos theta` and `y = b sin theta`, find `(dy)/(dx)` pics of allergic reactions on faceWeb21 sep. 2024 · Sine (sin): Sine of an angle is defined by the ratio of lengths of sides which is opposite to the angle and the hypotenuse. For the above triangle, the value of angle sine is given for both ∠A and ∠B, the definition for sine angle is … pics of all little orphan annie mugsWebIf X = A Sec θ Cos ϕ, Y = B Sec θ Sin ϕ And Z = C Tan θ, Show that X^2/A^2 + Y^2/B^2 - X^2/C^2 = 1 . CBSE English Medium Class 10. Question Papers 939. Textbook Solutions 33590. MCQ Online Mock Tests 12. Important Solutions 4010. Question Bank Solutions 26519. Concept Notes & Videos & Videos 213. pics of a line dressesWeb28 aug. 2024 · Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and … top car insurance 77627Web19 mei 2024 · If x = a cos θ and y = b sin θ, then b2x2 + a2y2 = A. a2b2 B. ab C. a4b4 D. a2 + b2 trigonometric identities class-10 1 Answer +1 vote answered May 19, 2024 by Maadesh (31.8k points) selected May 24, 2024 by Gaatrika Best answer Given: x = a sin θ and y = b cos θ ⇒ x2 = a2 sin2θ and y2 = b2 cos2θ ……… (i) To find: b2x2 + a2y2 pics of aliens on moonWebThe correct option is B sin 2 θ + cos 2 β Explanation for the correct option. Given that, sin - 1 ( x) = θ + β and sin - 1 ( y) = θ - β. ⇒ x = sin ( θ + β) and y = sin ( θ - β) 1 + x y = 1 + sin ( θ + β) sin ( θ - β) 1 + x y = 1 + sin 2 θ - sin 2 β Using the identity, sin 2 A + cos 2 A = 1. 1 + x y = sin 2 θ + cos 2 β Hence, option B is correct. pics of alicia keysWeb2 dec. 2024 · If x = a (1 + cos θ cos ϕ), y = b (1 + cos θ sin ϕ) and z = c (1 + sin θ), then which of the following is correct? (a) ( x−a a)2 ( x − a a) 2 + ( y−b b)2 ( y − b b) 2 + ( z−c c)2 ( z − c c) 2. (b) x2 a2 + y2 b2 + z2 c2 = 1 x 2 a 2 + y 2 b 2 + z … top car insurance 77707