What is the value of cos66° + sin84°?

To find the value of cos66° + sin84°, use trigonometric identities.

Step 1: Use Identity

sinθ = cos(90° − θ)

So,
sin84° = cos(6°)

Step 2: Substitute

Expression becomes:
cos66° + cos6°

Step 3: Use Formula

cosA + cosB = 2 cos[(A + B)/2] cos[(A − B)/2]

So,
= 2 cos(36°) cos(30°)

Step 4: Use Known Values

• cos30° = √3 / 2
• cos36° ≈ 0.809

Thus,
2 × 0.809 × (√3 / 2)
= 0.809 × √3
≈ 0.809 × 1.732 ≈ 1.40

Final Answer:

cos66° + sin84° ≈ 1.40

Conclusion:

By applying trigonometric identities, the value of cos66° + sin84° is approximately 1.40.