If sec(5 ∝ - 15°) = cosec ( 15° - 2 ∝), then value of cos 2∝ + sin 2∝ + tan (1.5∝):
Answer & explanation
Correct answer: option 1
If sec A = cosec B. then A + B = 90°
Hence,
⇒ 5 ∝ - 15° + 15° - 2 ∝ = 90°
⇒ 3 ∝ = 90°
⇒ ∝ = 30°
Now,
⇒ cos (60°) + sin (60°) + tan (\(\frac{3}{2}\) × 30°)
= \(\frac{1}{2}\) + \(\frac{\sqrt {3}}{2}\) + tan 45°
= \(\frac{1}{2}\) + \(\frac{\sqrt {3}}{2}\) + 1
= \(\frac{3}{2}\) + \(\frac{\sqrt {3}}{2}\)
= \(\frac{3 + \sqrt {3}}{2}\)