If tan 2 A - A -18- then the value of angle A in degrees isA- 36

The correct option is A 36Given: nbsp; nbsp;tan 2A = cot (A 18^∘) On rearranging nbsp;the equation with one trigonometric ratio on each side, we get ⇒ ...

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Standard IX

Mathematics

Complementary Ratios

If tan 2 A = ...

Question

If tan2A = cot(A- $18^{\circ}$ ), then the value of angle A in degrees is _____.
36

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Solution

The correct option is A 36
Given: tan 2A = cot (A - $18^{\circ}$ )

On rearranging the equation with one trigonometric ratio on each side, we get

$\Rightarrow$ tan 2A = tan (90 - (A - $18^{\circ}$ ))

$∵ t a n (90 ° - θ) = c o t θ$

$\Rightarrow$ tan 2A = tan ( $108^{\circ}$ - A)

$\Rightarrow$ 2A = $108^{\circ}$ - A

$\Rightarrow$ 3A = $108^{\circ}$

$\Rightarrow$ A = $36^{\circ}$

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If tan2A = cot(A-18∘), then the value of angle A in degrees is _____.36

The correct option is A 36Given: tan 2A = cot (A - 18∘) On rearranging the equation with one trigonometric ratio on each side, we get​ ⇒ tan 2A = tan (90 - (A - 18∘)) ∵tan(90°−θ)=cotθ ⇒ tan 2A = tan (108∘ - A) ⇒ 2A = 108∘ - A ⇒ 3A = 108∘ ⇒ A = 36∘

If tan2A = cot(A- $18^{\circ}$ ), then the value of angle A in degrees is _____.
36