Question

If sec 4A =cosec (A-20°) where 4A is an acute angle, find the value of A.

Answer 1

sec4A=cosec(A_20)
or,cosec(90_4A)=cosec(A_20)
or,90_4A=A_20
or ,5A=110
or,A=110/5=22ans.

Answer 2

$\bf\huge\underline{Question}$

If sec 4A =cosec (A-20°) where 4A is an acute angle, find the value of A.

$\bf\huge\underline{Answer}$

sec 4A = cosec (A - 20°)

Also, sec 4A = cosec (90° - 4A)

[Since, cosec (90° - θ) = sec θ]

Therefore, A - 20° = 90° - 4A

=> A + 20° = 90° + 20°

=> 5A = 110°

=> A = $\dfrac{110°}{5}$ = 22°