Question

Cos 70/sin 20 + cos 59/sin 31 - 8sin2^30

Answer 1

Answer:

(cos70°/sin20°) + (cos59°/sin31°) - 8 sin230°

Concept

Using

cos(90° - θ) = sinθ

sin(90° - θ) = cosθ

sin30° = (1/2)

Calculation

cos70° = cos(90° - 20°)

⇒ cos70° = sin20° and

⇒ cos59° = cos(90° - 31°)

⇒ cos59° = sin31°

Now, substitute the values in equation

⇒ (sin20°/sin20°) + (sin31°/sin31°) - 8sin230°

⇒ 1 + 1 - (8 × (1/2)2)

⇒ 2 - (8 × (1/4))

⇒ 2 - 2 = 0

∴ (cos70°/sin20°) + (cos59°/sin31°) - 8 sin230° = 0

Answer 2

Sin(90°-α) = cosα

cos(90°-α) = sinα

‏‏‎ ‎

So,

=cos70°/sin20°+cos59°/sin31°-8sin²30°

=[cos(90°-20)/sin20°+[cos(90°-31°)]/sin31°-8×(1/2)²

= sin20°/sin20°+sin31°/sin31°-2

= 1+1-2

= 0

[tex][/tex]