Question

The value of cos²15°-cos²30°+cos²45°-cos²60°+cos²75°​

Answer 1

$\huge\underline\green{ǫᴜᴇsᴛɪᴏɴ:-}$

The value of cos²15°-cos²30°+cos²45°-cos²60°+cos²75°

• Cos 75° = Cos (90° - 15°) = Sin 15°

• Cos² 15°+ Cos² 45° + Cos² 75°

• Therefore Cos² 75° = Sin² 15°

• Now, Cos² 15°+ Cos² 45° + Cos² 75°

• = Cos² 15°+ Cos² 45° + Sin² 15°

• = (Cos² 15° + Sin² 15°) + Cos² 45°

• = 1 + (1 / √2)² = 1 + (1 / 2) = 3/2

$\huge\underline\red{ᴘʀᴏᴠᴇᴅ}$