Question

The value of cos3 20°-cos3 70°/sin3 70°-sin3 20° is
A. 1/2
B. 1/√2
C. 1
D. 2

Answer 1

Given : cos³ 20° - cos³ 70°/ sin³ 70° - sin³ 20°

solution :

cos³ 20° - cos³ 70°/ sin³ 70° - sin³ 20°

= [(cos 20° - cos 70°) (cos² 20° + cos² 70° + cos 20° cos 70°)] / [(sin 70° - sin 20°)(sin² 70° + sin² 20°+ sin 70° sin 20°

[(a³ - b³) = (a -  b) (a² + b² + ab]

= [(cos (90° - 70°) - cos (90° - 20°)) (cos² (90° - 70°)+ cos² 70° + cos 20° cos 70°] / [(sin 70° - sin 20°)(sin² 70° + sin²(90° -  70°)) + sin (90° - 20° ) sin (90° - 70°)]

= (sin 70° - sin 20°)(sin² 70° + cos² 70° + cos 20° cos 70°] / [(sin 70° - sin 20°)(sin² 70° + cos ²  70°)) + cos 20° cos 70°)]

[cos (90 - θ) = sin θ , sin (90° -θ ) = cos θ]

= (1 + cos 20° cos 70°) / (1 + cos 20° cos 70°)

[sin² θ + cos²  θ = 1]

= 1

cos³ 20° - cos³ 70°/ sin³ 70° - sin³ 20° = 1

Hence, the value of cos³ 20° - cos³ 70°/ sin³ 70° - sin³ 20° is 1 .

The correct option is  (c) 1.

HOPE THIS ANSWER WILL HELP YOU……

 

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