Question

Assertion (A): If cos A + cos²A = 1, then sin²A + sin⁴A = 1.

Reason (R): sin²A + cos²A = 1.

Options

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

• Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).

• Assertion (A) is true but reason (R) is false.

• Assertion (A) is false but reason (R) is true.

Answer 1

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Explanation:

cos A + cos²A = 1   ...(i)

Gives cos A = sin²A   ...(ii) (Using sin²A + cos²A = 1)

Substituting value of cos A from (ii) in (i),

sin²A + sin⁴A = 1

∴ Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).