Assertion (A): If sin2 A + sin A = 1 then cos4 A + cos2 A = 1. Statement 2: 1 - sin2 A = cos2 A 1. (A) is true, (R) is false. 2. (A) is false, (R) is true. 3. Both (A) and (R) are true, and (R) is the correct reason for (A). 4. Both (A) and (R) are true, and (R) is the incorrect reason for (A).

Question

KnowledgeBoat · Accepted Answer

Given, ⇒ sin2 A + sin A = 1 ⇒ sin A = 1 - sin2 A ⇒ sin A = cos2 A Squaring both the sides, we get : ⇒ (sin A)2 = (cos2 A)2 ⇒ sin2 A = cos4 A ......................(1) Solving L.H.S. of cos4 A + cos2 A = 1, we get : ⇒ cos4 A + cos2 A ⇒ sin2 A + cos2 A [From equation (1)] ⇒ 1. Since, L.H.S. = R.H.S. ∴ Assertion (A) is true. As we know that, sin2 A + cos2 A = 1 ⇒ 1 - sin2 A = cos2 A ∴ Reason (R) is true. ∴ Both (A) and (R) are true, and (R) is the correct reason for (A). Hence, option 3 is the correct option.

Mathematics

Assertion (A): If sin² A + sin A = 1 then cos⁴ A + cos² A = 1.
Statement 2: 1 - sin² A = cos² A
(A) is true, (R) is false.
(A) is false, (R) is true.
Both (A) and (R) are true, and (R) is the correct reason for (A).
Both (A) and (R) are true, and (R) is the incorrect reason for (A).

Trigonometric Identities

Answer

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Mathematics

Assertion (A): If sin2 A + sin A = 1 then cos4 A + cos2 A = 1.Statement 2: 1 - sin2 A = cos2 A(A) is true, (R) is false.(A) is false, (R) is true.Both (A) and (R) are true, and (R) is the correct reason for (A).Both (A) and (R) are true, and (R) is the incorrect reason for (A).