Question

Find value of sin75°
(A) √3 − 1/2√2
(B) √3 + 1/2√2
(C) 2√2/√3 + 1
(D) √3/2

Answer 1

We can use the known identity

sin(A + B) = sinAcosB + sinBcosA

75° = (45° + 30°)

Hence,

sin(75°) = sin(45° + 30°)

→ sin45°cos30° + sin30°cos45°

Just put the values of these trigonometric ratios and voila!

(1/√2) × (1/2) + (√3/2) × (1/√2)

→ (√3 + 1)/(2√2)

Hence, the answer is choice B) (√3 + 1)/(2√2)

As easy as that!

Answer 2

Identity used :

• sin ( A + B ) = sin A cos B + cos A sin B

Solution :

$\tt \implies \sin75\degree \\ \\ \tt \implies \sin(30\degree + 45\degree) \\ \\ \tt \implies \sin30\degree \cos45\degree + \cos30\degree \sin45\degree \\ \\ \tt \implies \frac{1}{2} \times \frac{1}{ \sqrt{2} } + \frac{ \sqrt{3} }{2} \times \frac {1}{\sqrt{2} } \\ \\ \tt \implies \frac{1}{2 \sqrt{2} }+ \frac{ \sqrt{3} }{2 \sqrt{2} } \\ \\\tt \implies \frac{\sqrt{3} + 1}{2 \sqrt{2} }$

Option b is correct answer