If tan 4- cot-10- where 4- and-10- are acute angles then the value of - in degrees is

The correct option is A 20^∘Given, tan 4θ= cot(θ 10^∘) This can be written as cot(90^∘ 4θ)= cot(θ 10^∘) —–(i) (∵ Tan θ = Cot(90^∘ θ)) Hence, from (i) ...

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Standard X

Mathematics

Trigonometric Identities

If tan 4θ= co...

Question

If $t a n 4 θ = c o t (θ - 10^{\circ})$ , where $4 θ$ and $(θ - 10^{\circ})$ are acute angles then the value of $θ$ in degrees is

16^{\circ}

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20^{\circ}

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32^{\circ}

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40^{\circ}

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Solution

The correct option is B $20^{\circ}$
Given, $t a n 4 θ = c o t (θ - 10^{\circ})$

This can be written as

$c o t (90^{\circ} - 4 θ) = c o t (θ - 10^{\circ})$ -----(i)

$(∵$ $T a n θ$ = $C o t (90^{\circ} - θ))$

Hence, from (i) we have

$\Rightarrow 90^{\circ} - 4 θ = θ - 10^{\circ}$
$\Rightarrow 5 θ = 100^{\circ}$
$\Rightarrow θ = 20^{\circ}$

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If tan 4θ=cot(θ−10∘), where 4θ and(θ−10∘) are acute angles then the value of θ in degrees is

The correct option is B 20∘Given, tan 4θ=cot(θ−10∘) This can be written as cot(90∘− 4θ)=cot(θ−10∘) -----(i) (∵ Tan θ = Cot(90∘− θ)) Hence, from (i) we have ⇒90∘− 4θ= θ−10∘ ⇒5θ =100∘ ⇒θ =20∘

If $t a n 4 θ = c o t (θ - 10^{\circ})$ , where $4 θ$ and $(θ - 10^{\circ})$ are acute angles then the value of $θ$ in degrees is