In a Δ A B C , a b = 2 + 3 , and ∠ C = 60 ° . Then the ordered pair ( ∠ A , ∠ B…

In a ΔABC, ab=2+3, and ∠C=60°. Then the ordered pair (∠A,∠B) is equal to:
  1. 105°, 15°
  2. 15°, 105°
  3. 45°, 75°
  4. (75°, 45°)

Solution

ab>1⇒∠A>∠B

A+B=120°

⇒sin(120°−B)sinB=2+3

⇒  32cotB+12=2+3

⇒ cotB=2332+3

 ⇒cotB=2+3

⇒   B=15°

Hence, (∠A,∠B)=(105°,15°)

Asked in: JEE Main 2015 (10 Apr Online)

Practice more Trigonometric Ratios & Identities questions on Aicharya