Question

if sec 4A=cosec[A-20],where 4A is an acute angle,find the value of A

Answer 1

Step-by-step explanation:

sec 4A = cosec (A-20)

since,

sec4A= cosec (90-4A)

= cosec(90-4A)=cosec(A-20)

90-4A and A-20 are both acute angles therefore

90-4A =A-20

90+20= A+4A

110 = 5A

A= 22

Answer 2

QUESTION :-

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

SOLUTION :-

sec 4A = cosec(A - 20°)  

⇒cosec(90° - 4A) = cosec(A - 20°)

As cosec(90° - A) = secA, and vice-versa.

⇒90° - 4A = A - 20°

Same bases get cancelled.

⇒90° + 20° = A + 4A

⇒110° = 5A

⇒A = 110°/5

⇒A = 22°