Question:
If tan θ = 7/24, then find the value of (cos^2 θ – sin^2 θ).
यदि tan θ = 7/24 है, तो (cos^2 θ – sin^2 θ) का मान ज्ञात कीजिए।
Options:
- a) 529/625
- b) 576/625
- c) 527/625
- d) 1
- a) 529/625
- b) 576/625
- c) 527/625
- d) 1
correct answer : c)
Explanation:
Given tan θ = 7/24. Since tan θ = Opposite/Adjacent, Hypotenuse = sqrt(7^2 + 24^2) = sqrt(49 + 576) = 25. Thus, sin θ = 7/25 and cos θ = 24/25. The value of cos^2 θ – sin^2 θ = (24/25)^2 – (7/25)^2 = (576 – 49)/625 = 527/625.
दिया गया है tan θ = 7/24। चूँकि tan θ = लम्ब/आधार, कर्ण = sqrt(7² + 24²) = sqrt(49 + 576) = 25। इस प्रकार, sin θ = 7/25 और cos θ = 24/25। cos² θ – sin² θ का मान = (24/25)² – (7/25)² = (576 – 49)/625 = 527/625 है।