Question

Show that tan46 tan26 tan44 tan64 is equal to 1.​

Answer 1

Answer:

they'll cancel out... leaving 1

Step-by-step explanation:

=cot44.cot64.tan44.tan64

=tan44/cot44. ×tan64/cot64

=1

Answer 2

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

Step-by-step explanation:

To 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,

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

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

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

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.