The value oftan 48- - tan 23-tan 42-tan 67- is equal to

The correct option is B 1tan48^∘.tan23^∘.tan42^∘.tan67^∘ We know that cot(90^∘ θ) = tanθ ∴ tan48^∘.tan23^∘.tan42^∘.tan67^∘ = tan48^∘.tan23^∘.cot(90^∘ 42^ ...

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Byju's Answer

Standard X

Mathematics

Introduction to Trigonometry

The value oft...

Question

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

0.0

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Solution

The correct option is B 1
$t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}$

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

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tan 7^{\circ} tan 23^{\circ} tan 60^{\circ} tan 67^{\circ} tan 83^{\circ}

Q. Find the value of the

\frac{s i n 17^{\circ} s e c 73^{\circ} - c o s e c^{2} 67^{\circ}}{s e c^{2} 45^{\circ} - t a n 23^{\circ} t a n 67^{\circ} + c o t^{2} 67^{\circ}}

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

tan 48^{\circ} . tan 23^{\circ} . tan 42^{\circ} . tan 67^{\circ}

= ___

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The value of tan 48∘.tan 23∘.tan 42∘.tan 67∘ is equal to

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