Question

2tan23 tan35 tan30 tan55 tan67

Answer 1

Answer: 2/root 3

Step-by-step explanation:

tan23.tan67=1

tan35.tan55=1

tan30=1/root3

Answer 2

The simplification of the given equation is $\frac{2}{\sqrt{3}}$

Step-by-step explanation:

given :

$2\tan 23\times \tan 35 \times \tan 30 \times \tan 55 \times \tan67$

we know that

$(\tan 90 - \theta )= \cot \theta$

therefore

$2\tan (90-67)\times \tan (90-55) \times \tan 30 \times \tan 55 \times \tan67 \\\\2 \cot 67 \times \cot 55 \times \tan 30 \times \tan 55 \times \tan67$

also

$\tan \theta = \frac{1}{\cot \theta}$

thus ,

$2 \cot 67 \times \cot 55 \times \tan 30 \times \tan 55 \times \tan67\\\\2 \times \frac{1}{ \tan67}\times \frac{1}{ \tan 55}\times\tan 30 \times \tan 55 \times \tan67\\\\ 2 \tan 30\\\= 2\times \frac{1}{\sqrt{3}}\\\\=\frac{2}{\sqrt{3}}$

hence , The simplification of the given equation is $\frac{2}{\sqrt{3}}$

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