The value of the expression (1/2) ( √3 sin 75° - cos 75° ) is :

Question

The value of the expression (1/2) ( √3 sin 75° - cos 75° ) is : (A) 1 (B) 2 (C) 1 / √2 (D) 2 / √2

Tardigrade Admin · Accepted Answer

Consider (1/2) (√3 sin75° - cos75°) = (√3/2) . sin 75° - (1/2) cos75° = sin60°. sin75° - cos60°. cos75° = - [ cos(75°+ 60°)] = - cos135 ° = - cos(180° - 45°) = + (1/√2)

Q. The value of the expression $\frac{1}{2} (3 sin 7 5^{\circ} - cos 7 5^{\circ})$ is :

1

2

$1/ 2$

$2/ 2$

Q. The value of the expression 21​(3​sin75∘−cos75∘) is :

1

2

1/2​

2/2​

Consider 21​(3​sin75∘−cos75∘) =23​​.sin75∘−21​cos75∘ =sin60∘.sin75∘−cos60∘.cos75∘ =−[cos(75∘+60∘)] =−cos135∘ =−cos(180∘−45∘) =+2​1​

Q. The value of the expression $\frac{1}{2} (3 sin 7 5^{\circ} - cos 7 5^{\circ})$ is :

$1/ 2$

$2/ 2$