Find the value of tan 48-tan 23-tan 42-tan 67- -

Tan48^∘.tan23^∘.tan42^∘.tan67^∘ nbsp; We know that cot(90^∘ θ) = tanθ ∴ nbsp;tan48^∘.tan23^∘.tan42^∘.tan67^∘ nbsp; = tan48^∘.tan23^∘.cot(90^∘ 42^∘).co ...

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Byju's Answer

Standard X

Mathematics

Introduction to Trigonometry

Find the valu...

Question

Find the value of
$t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}$ .

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Solution

$t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}$

We know that $c o t (90^{\circ} - θ) = t a n θ$

$∴ t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}$
= $t a n 48^{\circ} . t a n 23^{\circ} . c o t (90^{\circ} - 42^{\circ}) . c o t (90^{\circ} - 67^{\circ})$
= $t a n 48^{\circ} . t a n 23^{\circ} . c o t 48^{\circ} . c o t 23^{\circ}$

We also know that $t a n θ \times c o t θ = 1$

$∴ t a n 48^{\circ} . t a n 23^{\circ} . c o t 48^{\circ} . c o t 23^{\circ}$
= $t a n 48^{\circ} . c o t 48^{\circ} . t a n 23^{\circ} . c o t 23^{\circ}$
= $1 \times 1$
= 1

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Similar questions

The value of
$t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}$ =___

t a n 48^{\circ} t a n 23^{\circ} t a n 42^{\circ} t a n 67^{\circ} =

t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}

Q. The value of

t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}

is equal to

Q. Show that :

tan 48^{o} tan 23^{o} tan 42^{o} tan 67^{o} = 1

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Find the value of tan 48∘.tan 23∘.tan 42∘.tan 67∘ .

Find the value of
$t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}$ .