If tan 2A - cot A - 18- where 2A is an acute angle- find the value of A-2 marks-

Tan 2A = cot (A 18^∘) ⇒ cot (90^∘ 2A) = cot (A 18^∘) (As tan A = cot (90^∘ A)) [1 mark] Equating angles, ⇒ 90^∘ 2A = A 18^∘ ⇒ 108^∘ = 3A ⇒ A = 36^∘ ...

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Standard X

Mathematics

Trigonometric Identities

If tan 2A = c...

Question

If $t a n 2 A = c o t (A - 18^{\circ})$ , where 2A is an acute angle, find the value of A.
[2 marks]

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Solution

$t a n 2 A = c o t (A - 18^{\circ})$
$\Rightarrow c o t (90^{\circ} - 2 A) = c o t (A - 18^{\circ})$
(As tan A = cot ( $90^{\circ}$ - A))
[1 mark]

Equating angles,

$\Rightarrow 90^{\circ} - 2 A = A - 18^{\circ} \Rightarrow 108^{\circ} = 3 A \Rightarrow A = 36^{\circ}$

[1 mark]

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If tan2A=cot(A−18∘), where 2A is an acute angle, find the value of A. [2 marks]

tan2A=cot(A−18∘) ⇒cot(90∘−2A)=cot(A−18∘) (As tan A = cot (90∘ - A)) [1 mark] Equating angles, ⇒90∘−2A=A−18∘⇒108∘=3A⇒A=36∘ [1 mark]

If $t a n 2 A = c o t (A - 18^{\circ})$ , where 2A is an acute angle, find the value of A.
[2 marks]

$t a n 2 A = c o t (A - 18^{\circ})$
$\Rightarrow c o t (90^{\circ} - 2 A) = c o t (A - 18^{\circ})$
(As tan A = cot ( $90^{\circ}$ - A))
[1 mark]

Equating angles,

$\Rightarrow 90^{\circ} - 2 A = A - 18^{\circ} \Rightarrow 108^{\circ} = 3 A \Rightarrow A = 36^{\circ}$

[1 mark]