If sec 2A = cosec (A-42), where 2A is an acute angle, find the value o

1.	If sec 2A = cosec (A-42), where 2A is an acute angle, find the value of A.
Answer» Sec2A=cosec(A-42°)or, cosec(90°-2A)=cosec(A-42°) [∵, cosec(90°-θ)=secθ]or, 90°-2A=A-42°or, -2A-A=-42°-90°or, -3A=-132°or, A=132°/3or, A=44° Sec2A=cosec(A-42) then, Sec2A=cosec(90-2A) ,cosec(90-2A)=cosec(A-42) ,90-2A=A-42,3A=132,A=44 Cosec(90-2A) =cosec(A-42)90-2A = A-4290+42 = A+2A132 = 3AA= 44.

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