What is the value of 3 − (sin 239° + sin 251°)?
3 − (sin 239° + sin 251°) का मान ज्ञात कीजिए।
This Question Asked In:
SSC, CGL MAINS 2026
Correct Answer :A - 3
Detailed Text Solution
We use the identity:
sin(180° + θ) = −sinθ.
239° = 180° + 59°
So, sin239° = −sin59°.
251° = 180° + 71°
So, sin251° = −sin71°.
Thus,
sin239° + sin251° = −(sin59° + sin71°).
Using identity:
sinA + sinB = 2 sin((A+B)/2) cos((A−B)/2).
= 2 sin(65°) cos(−6°)
= 2 sin65° cos6°.
Since sin65° ≈ 0.9063 and cos6° ≈ 0.9945,
Product ≈ 2 × 0.9063 × 0.9945 ≈ 1.803.
So sin239° + sin251° ≈ −1.803.
Therefore,
3 − (−1.803) ≈ 4.803 ≈ 4 (nearest option).