Question

Assertion (A): If A = 30°, the value of 4 sin A sin (60° − A) sin (60° + A) = 1.

Reason (R): 60° − A = 30° and 60° + A = 90°.

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:

Substituting A = 30°:

\[4 \sin 30^\circ \sin(60^\circ - 30^\circ) \sin(60^\circ + 30^\circ) = 4 \left(\frac{1}{2}\right) \sin 30^\circ \sin 90^\circ\]

= \[4 \left(\frac{1}{2}\right) \left(\frac{1}{2}\right) (1) = 1\]

Both the assertion and the reason are true, with R correctly breaking down the angle values used in the calculation.