Question

Evaluate: $\frac{cos80\textdegree}{sin10\textdegree} +cos 59\textdegree . cosec 31\textdegree - cosec^245\textdegree$

Answer 1

Answer:

0

Step-by-step explanation:

$\frac{cos 80°}{sin 10°}$ + cos 59°. cosec 31° - cosec² 45°.

$\frac{cos (90°-10°)}{sin 10°}$ + cos (90°-31°). cosec 31° - cosec² 45°.

$\frac{sin 10°}{sin 10°}$ + sin 31°. cosec 31° - cosec² 45°.

or, 1 + 1 - (√2)²

or, 2 - 2 = 0. [Ans]

We have used a basic formula of Trigonometrical identities:

cos(90° - θ) = sin θ.

Also we know the value of cosec 45° = √2.

Answer 2

Solution :

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i ) cos80° = cos( 90 - 10 )

= sin 10°

ii ) cos 59 = cos( 90 - 31 )

= sin 31°

iii ) sin31° × cosec 31° = 1

iv ) cosec 45 = √2
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Now ,

(cos80°/sin10° )+cos59cosec31-cosec²45

= ( sin10/sin10) + sin31cosec31 - ( √2 )²

= 1 + 1 - 2

= 0

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