Question

Find the value of cos20°/sin70° + cos70°/sin20° - 8sin^2 30°

Answer 1

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Answer 2

(cos20°/sin70°) + (cos70°/sin20°) - 8(sin²30°)

=cos(90°-70°)/sin70°  +  cos(90°-20°)/sin20°  -  8sin²30°

= (sin70°/sin70°) + (sin20°/sin20°) - 8sin²30°    

[using the property: cos(90°-θ) = sinθ]

= 1 + 1 - 8×(1/2)×(1/2)

[using sin30° = 1/2]

= 1 + 1 - 2

=0.

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