Question

sin 25° / cos 65° + cosec 34°/ sec 56° - 2cos 43° cosec 47° / tan 10° • tan 40° • tan 50° • tan 80°​

Answer 1

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Answer 2

The answer to the given trigonometrical expression is 0.

Given,

The trigonometrical expression = $\frac{sin25}{cos65} +\frac{cosec34}{sec56}-\frac{2cos43 * cosec47}{tan10*tan40*tan50*tan80}$

To Find,

The value of the given trigonometrical expression.

Solution,

Now, let's solve the question using trigonometrical identities.

= $\frac{sin25}{cos65} +\frac{cosec34}{sec56}-\frac{2cos43 * cosec47}{tan10*tan40*tan50*tan80}$.

Now, we will use trigonometrical identities,

cos(90 - θ) = sinθ

sec(90 - θ) = cosecθ

tan(90 - θ) = cotθ

=  $\frac{sin25}{sin25} +\frac{cosec34}{cosec34}-\frac{2cos43 * sec43}{cot80*tan40*cot40*tan80}$

on eliminating, we get,

= 1 + 1 $\frac{2cos43\frac{1}{cos43} }{tan80\frac{1}{tan80}tan40 \frac{1}{tan40} }$.

We know that secθ = 1/cosθ and cotθ = 1/tanθ

On solving, we get,

= 1 + 1 -2

= 2 - 2

= 0.

The answer to the given trigonometrical expression is 0.

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