Question

Statement (1): The angle C of a right-angled triangle is 90°; then tan A = cot B.

Statement (2): Since angle C of triangle ABC = 90°. ∴ ∠A + ∠B = 90° ⇒ ∠A = 90° − ∠B.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

Since ∠A + ∠B = 90°, we have ∠A = 90° − ∠B. Taking the tangent on both sides gives tan A = tan(90° − B) = cot B. Hence, both statements are true and Statement 2 correctly leads to Statement 1.