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
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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.
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