Question

Assertion (A): If sin A `1/3` (0° < A < 90°), then the value of cos A is `(2sqrt2)/3`.

Reason (R): For every angle θ, sin²θ + cos²θ = 1.

Options

• Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true. Reason (R) does not give correct explanation of (A).

• Assertion (A) is true but Reason (R) is not true. 

• Assertion (A) is not true but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A). 

Explanation:

Given, sin A = `1/3`

Here, sin A = `"perpendicular"/"Hypotenuse"`

We know that H² = P² + B²

⇒ (3)² = (1)² + B² 

⇒ 9 − 1 = B² 

B = `2sqrt2`

cos A = `"Base"/"Hypotenuse"`

cos A = `(2sqrt2)/3 ->"True"`

Reason: When θ is equal

then sin² θ+ cos² θ = 1

⇒ H² = p² + B²

⇒ `H^2/H^2 = P^2/H^2 + B^2/H^2`

⇒ [1 = sin² θ + cos² θ] → True