Question

If Tan 5A=cot (2A+6), where 5A is an acute angle, then find
the value of 'A'.​

Answer 1

$Given \: tan \:5A = cot \:(2A+6)$

$\implies tan 5A = tan [ 90 - ( 2A +6) ]$

$\boxed { \pink { Since, cot \theta = tan (90 - \theta) }}$

$\implies 5A = 90 - (2A + 6 )$

$\implies 5A = 90 - 2A - 6$

$\implies 5A + 2A = 84$

$\implies 7A = 84$

$\implies A = \frac{84}{7}$

$\implies A = 12$

Therefore.,

$\red { Value \:of \: A } \green { = 12\degree }$

•••♪

Answer 2

$\huge\bold\green{Question}$

If Tan 5A=cot (2A+6), where 5A is an acute angle, then find

the value of 'A'

$\huge\bold\green{Answer}$

→ Value of A = 12°

According to the question we have given :-

•°• Tan 5A = Cot ( 2A + 6 )

As we know that :-

By changing Cot∅ into Tan∅ [Cot∅=Tan (90−∅) ]

= Tan5A = Tan [ 90− (2A+6) ]

Now by cancelling " Tan" both sides

= 5A = 90 − ( 2A + 6 )

= 5A = 90 - 2A - 6

= 5A + 2A = 96 - 6

= 5A + 2A = 84

= 7A = 84

= A = ${\cancel\frac{84}{7}}$

= A = 12

Hence the required value of " A " is 12°