Trigonometry
- The value of (sin² 25° + sin² 65°) is :
-
View Hint View Answer Discuss in Forum
sin² 25° + sin² 65°
= sin² 25° + sin² (90° - 25°)
= sin² 25° + cos² 25° = 1Correct Option: B
sin² 25° + sin² 65°
= sin² 25° + sin² (90° - 25°)
= sin² 25° + cos² 25° = 1
- The value of cos 1° cos 2° cos 3°....... cos 177° cos 178° cos 179° is :
-
View Hint View Answer Discuss in Forum
cos 90° = 0
∴ cos 1°. cos 2° ... cos 179° = 0Correct Option: A
cos 90° = 0
∴ cos 1°. cos 2° ... cos 179° = 0
-
If sec θ = x + 1 (0° < θ < 90°), then sec θ + tan θ is equal to 4x
-
View Hint View Answer Discuss in Forum
sec θ = 4x² + 1 4x
tan θ = √sec² θ - 1
√[(4x² + 1 / 4x)²] - 1
√[(4x² + 1)² - (4x)² / (4x)²](2x + 1)(2x - 1) = 4x² - 1 4x 4x ∴ sec θ + tan θ = 4x² + 1 + 4x² - 1 4x 4x = 4x² + 1 + 4x² - 1 4x = 8x² = 2x 4x
Correct Option: B
sec θ = 4x² + 1 4x
tan θ = √sec² θ - 1
√[(4x² + 1 / 4x)²] - 1
√[(4x² + 1)² - (4x)² / (4x)²](2x + 1)(2x - 1) = 4x² - 1 4x 4x ∴ sec θ + tan θ = 4x² + 1 + 4x² - 1 4x 4x = 4x² + 1 + 4x² - 1 4x = 8x² = 2x 4x
- If 7 sin²θ+ 3 cos²θ= 4 (0° ≤ θ ≤ 90°), then value of θ is
-
View Hint View Answer Discuss in Forum
7 sin²θ + 3 cos²θ = 4
⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
⇒ 7 sin²θ + 3 – 3 sin²θ = 4
⇒ 4 sin²θ = 4 – 3 = 1⇒ sin²θ = 1 4 ⇒ sinθ = 1 = sin π 2 6 ⇒ θ = π 6
Correct Option: C
7 sin²θ + 3 cos²θ = 4
⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
⇒ 7 sin²θ + 3 – 3 sin²θ = 4
⇒ 4 sin²θ = 4 – 3 = 1⇒ sin²θ = 1 4 ⇒ sinθ = 1 = sin π 2 6 ⇒ θ = π 6
- If 7 sin²θ+ 3 cos²θ= 4 (0° ≤ θ ≤ 90°), then value of θ is
-
View Hint View Answer Discuss in Forum
7 sin²θ + 3 cos²θ = 4
⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
⇒ 7 sin²θ + 3 – 3 sin²θ = 4
⇒ 4 sin²θ = 4 – 3 = 1⇒ sin²θ = 1 4 ⇒ sinθ = 1 = sin π 2 6 ⇒ θ = π 6
Correct Option: C
7 sin²θ + 3 cos²θ = 4
⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
⇒ 7 sin²θ + 3 – 3 sin²θ = 4
⇒ 4 sin²θ = 4 – 3 = 1⇒ sin²θ = 1 4 ⇒ sinθ = 1 = sin π 2 6 ⇒ θ = π 6