Prove that tan 6-tan 42-tan 66-tan 78-1

LHS = tan 6 tan 42 tan 66 tan 78 tan x tan (60 x) tan (60 + x) = tan x (standard fomula) Let x = 18 ⇒ tan 18 tan (60 18) tan (60 + 18) = tan n(3 × 18) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

Prove that ta...

Question

Prove that $t a n 6^{\circ} t a n 42^{\circ} t a n 66^{\circ} t a n 78^{\circ} = 1$

Open in App

Solution

LHS = tan 6 tan 42 tan 66 tan 78
tan x tan (60 - x) tan (60 + x) = tan x - (standard fomula)
Let x = 18
$\Rightarrow t a n 18 t a n (60 - 18) t a n (60 + 18) = t a n n (3 \times 18)$
tan 18 tan 42 tan 78 = tan 54
tan 42 tan 78 = $\frac{t a n 54}{t a n 18}$
Let x = 6
tan 6 tan(60 - 6) tan (60 + 6) = tan 18
tan 6 tan 54 tan 66 = tan 18
$\Rightarrow t a n 6 t a n 66 = \frac{t a n 54}{t a n 18} \times \frac{t a n 18}{t a n 54} = 1$
Hence proved

Suggest Corrections

Similar questions

tan6*tan42*tan66*tan78=1

Q. The value of:

tan 6^{\circ} tan 42^{\circ} tan 66^{\circ} tan 78^{\circ}

Q. The value of

tan 6^{\circ} tan 42^{\circ} tan 66^{\circ} tan 78^{\circ}

The value of tan6*tan42*tan66*tan78 is

Q. Prove that

\frac{\tan 69 ° + \tan 66 °}{1 - \tan 69 ° \tan 66 °} = - 1

Join BYJU'S Learning Program

Prove that tan 6∘tan 42∘tan 66∘tan 78∘=1

Prove that $t a n 6^{\circ} t a n 42^{\circ} t a n 66^{\circ} t a n 78^{\circ} = 1$