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
  • A. 3
  • B. 4
  • C. 2
  • D. 5
Correct Answer :A - 3
Detailed Solution Video
Video Credit –Nikhil Sharma Maths
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).

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