Question

Show that tan 46 tan 26 tan 44 tan 64 =1.​

Answer 1

Answer:

We know that tan theta is equal to cot 90 degree minus theta. By using this formula we can easily solve the above sum. Detailed answer is given in the attachment

Answer 2

$\tan 46 \tan 26 \tan 44 \tan 64=1$, shown.

Step-by-step explanation:

Show that $\tan 46 \tan 26 \tan 44 \tan 64=1$.

L.H.S. = $\tan 46 \tan 26 \tan 44 \tan 64$

$= \tan 46 \tan 26 \tan (90-46) \tan (90-26)$

Using the trigonometric identity,

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

$= \tan 46 \tan 26 \cot 46 \cot 26$

$= (\tan 46\cot 46) (\tan 26 \cot 26)$

$= (\tan 46.\dfrac{1}{\tan 46}) (\tan 26.\dfrac{1}{\tan 26})$

Using the trigonometric identity,

$\cot A=\dfrac{1}{\tan A}$

= (1)(1)

= 1

= R.H.S, shown.

Thus, $\tan 46 \tan 26 \tan 44 \tan 64=1$, shown.