Find the value of sin² 90° + cos² 60°.

Correct — A. sin²90° means (sin 90°)², so square each standard value and add.

Square sin 90° = 1: sin²90° = 1
Square cos 60° = 1⁄2: cos²60° = 1⁄4
Add: 1 + 1⁄4 = 5⁄4 → option (a)

Why the others are wrong

• (b)
  11⁄5 — 11⁄5 = 2.2, but a squared sine or cosine is never more than 1. Two such terms cannot add to more than 2.
• (c)
  6⁄5 — 6⁄5 is counted in fifths, but the two terms here are 1 and 1⁄4. Their sum can only be a whole number of quarters.
• (d)
  7⁄4 — 7⁄4 = 1 + 3⁄4 takes cos²60° as 3⁄4. That is cos²30°, the square of √3⁄2. cos 60° = 1⁄2, so its square is 1⁄4.

The sines of 0°, 30°, 45°, 60° and 90° follow one pattern: √0⁄2, √1⁄2, √2⁄2, √3⁄2, √4⁄2, that is 0, 1⁄2, 1⁄√2, √3⁄2, 1.

Cosines run the same list backwards, from 1 at 0° down to 0 at 90°. So sin 90° = 1 and cos 60° = 1⁄2, and their squares are 1 and 1⁄4.

Key facts

• sin 90° = 1 and cos 90° = 0.
• cos 60° = sin 30° = 1⁄2, and cos 30° = sin 60° = √3⁄2.
• sin²θ + cos²θ = 1 holds for one angle θ. With two different angles it need not hold.

Common traps

• Taking cos 60° as √3⁄2, the value of cos 30°, which leads to 7⁄4.
• Reading sin²90° as sin(90²) instead of (sin 90°)².
• Assuming a squared sine plus a squared cosine is always 1, even with two different angles.

No directly related past PYQ was found.