If M = x cos A + y sin A and N = x sin A - y cos A, then M 2 + N 2 is : 1. x 2 - y 2 2. y 2 - x 2 3. x 2 + y 2 4. (x + y) 2

Substituting value of M and N in M 2 + N 2 , we get : ⇒ (x cos A + y sin A) 2 + (x sin A - y cos A) 2 ⇒ x 2 cos 2 A + y 2 sin 2 A + 2xy sin A cos A + x 2 sin 2 A + y 2 cos 2 A - 2xy sin A cos A ⇒ x 2 cos 2 A + y 2 sin 2 A + x 2 sin 2 A + y 2 cos 2 A ⇒ x 2 cos 2 A + x 2 sin 2 A + y 2 sin 2 A + y 2 cos 2 A ⇒ x 2 (sin 2 A + cos 2 A) + y 2 (sin 2 A + cos 2 A) Substituting, sin 2 A + cos 2 A = 1, we get : ⇒ x 2 × 1 + y 2 × 1 ⇒ x 2 + y 2 . Hence, Option 3 is the correct option.

Mathematics

If M = x cos A + y sin A and N = x sin A - y cos A, then M² + N² is :
x² - y²
y² - x²
x² + y²
(x + y)²

Trigonometric Identities

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Answer

Substituting value of M and N in M² + N², we get :

⇒ (x cos A + y sin A)² + (x sin A - y cos A)²

⇒ x² cos² A + y² sin² A + 2xy sin A cos A + x² sin² A + y² cos² A - 2xy sin A cos A

⇒ x² cos² A + y² sin² A + x² sin² A + y² cos² A

⇒ x² cos² A + x² sin² A + y² sin² A + y² cos² A

⇒ x² (sin² A + cos² A) + y² (sin² A + cos² A)

Substituting, sin² A + cos² A = 1, we get :

⇒ x² × 1 + y² × 1

⇒ x² + y².

Hence, Option 3 is the correct option.

Answered By

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Mathematics

If M = x cos A + y sin A and N = x sin A - y cos A, then M² + N² is :
x² - y²
y² - x²
x² + y²
(x + y)²

Trigonometric Identities

Answer

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If M = x cos A + y sin A and N = x sin A - y cos A, then M2 + N2 is :x2 - y2y2 - x2x2 + y2(x + y)2

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