Question

if tan 2A = cot (A-18•) ,where 2A is an acute angle then find the value of A​

Answer 1

ANSWER

Given tan2A=cot(A−18

0

)

⇒cot(90−2A)=cot(A−18

0

)[∵tanθ=cot(90−θ)]

Comparing angles we get

90−2A=A−18

⇒90+18=A+2A

⇒3A=108

⇒A=

3

108

⇒A=36

∘

Answer 2

↬ Given :-

• tan 2A = cot (A - 18°)

• 2A is an acute angle

↬To find :-

• The value of A.

↬ Solution :-

$\rm\:tan\:2A=cot(A-18\degree)$

$\rm\longrightarrow\:cot(90-2A)=cot(A-18)$

$\rm\longrightarrow\:90-2A=A-18$

$\rm\longrightarrow\:90+18=A+2A$

$\rm\longrightarrow\:108=3A$

$\rm\longrightarrow\:\cancel\dfrac{108}{3}=A$

$\rm\longrightarrow\:A=36\degree$

Hence,the value of A is 36°.

$\underbrace{\bf\:More\:Information}$

➝ Trigonometry :- It is that branch of mathematics which deals with the measurement of angles and the problems allied with angles.

⸕ Some trigonometric identities

• Sin²θ + cos²θ = 1

• 1 + tan²θ = sec²θ

• 1 + cot²θ = cosec²θ

• tanθ = sinθ/cosθ

• cotθ = cosθ/sinθ

• tanθ × cotθ = 1