Question

Assertion(A): If sin² A + Sin A = 1 then cos⁴A + cos² A = 1

Reason(R): 1 − Sin²A = Cos²A

Options

• (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).

Answer 1

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

sin A = cos² A

[∴ cos²A = 1 − sin² A]

On squaring both sides, we get

⇒ sin² A = cos⁴ A

1 − cos² A = cos⁴ A

cos⁴ A + cos² A = 1