Question

sin A = cos A and tan² A + cot² A + 2.

Statement (1): A = 45°

tan² A + cot² A + 2 = 4

Statement (2): sin A = cos A ⇒ A = 45°

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:

Given, sin A = cos A

\[\Rightarrow \frac{\sin A}{\cos A} = 1\]

⇒ tan A = 1

⇒ tan A = tan 45°

⇒ A = 45°

So, statement 2 is true.

Substituting value of A in tan² A + cot² A + 2, we get:

⇒ tan2 A + cot2 A + 2 = tan2 45° + cot2 45° + 2

= (1)² + (1)² + 2

= 1 + 1 + 2

= 4.

So, statement 1 is true.

∴ Both the statements are true.