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The value of cot θ.tan(90° – θ) – sec(90° – θ) cosecθ + (sin² 25° + sin2 65°) + √3 (tan 5° tan 15°. tan 30°. tan75°. tan 85°) is :
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- 1
- - 1
- 2
- 0
Correct Option: A
cotθ. tan (90° – θ) – sec (90° – θ). cosecθ + (sin² 25° + sin² 65°) + √3(tan5°. tan15°. tan30°. tan75°. tan85°)
= cotθ.cotθ – cosecθ. cosecθ + (sin² 25° + cos² 25°) + √3 (tan 5°. cot 5°. tan15°. cot15°. tan30°)
= (cot2θ – cosec2θ) + (sin² 25° + cos² 25°) + √3 × (1 / √3)
= – 1 + 1 + 1 = 1
[sin(90° – θ) = cos θ; cosec² θ – cot² θ = 1; tan (90° – θ) = cotθ ; sec (90° – θ) = cosecθ]
