Question

Assertion (A): The value of sin² 30° − 2 cos³ 60° + 2 tan⁴ 45° is 2.

Reason (R): sin 30° = `1/2`, cos 60° = `1/2`, and tan 45° = 1.

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:

Evaluating the expression using the values in Reason R:

\[\left(\frac{1}{2}\right)^2 - 2\left(\frac{1}{2}\right)^3 + 2(1)^4 = \frac{1}{4} - 2\left(\frac{1}{8}\right) + 2 = \frac{1}{4} - \frac{1}{4} + 2 = 2\]

Thus, both Assertion and Reason are true, and Reason R provides the correct values.