QQuestion
Assertion (A): If sin² A + sin A = 1, then cos⁴ A + cos² A = 1.
Reason (R): 1 − sin² A = cos² A.
(a) A is true, R is false.
(b) A is false, R is true.
(c) Both A and R are true, and R is the correct reason for A.
(d) Both A and R are true, and R is not the correct reason for A.
✓Answer
(c) Both A and R are true, and R is the correct reason for A.
Explanation:
Given: sin² A + sin A = 1
⇒ sin A = 1 − sin² A
Using 1 − sin² A = cos² A:
sin A = cos² A
Squaring both sides:
sin² A = cos⁴ A … (1)
Now: cos⁴ A + cos² A
= sin² A + cos² A, using (1)
= 1
Thus, the assertion is true. The reason is also true and is used directly to prove the assertion.
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