Question

if sec 2A = cosec (A – 27°) where 2A is an acute angle, find the measure of ∠A.

Answer 1

Step-by-step explanation:

Given:-

sec 2A = cosec (A – 27°) where 2A is an acute angle

To find:-

if sec 2A = cosec (A – 27°) where 2A is an acute angle, find the measure of ∠A.

Solution:-

Given equation is sec 2A = cosec (A – 27°)

we know that Sec A = Cosec (90-A)

=> Cosec (90-2A)=Cosec (A-27°)

=>90-2A=A-27°

=>2A+A=90°+27°

=>3A=117°

=>A=117°/3

=>A=39°

Answer:-

The value of ∠A =39°

Check:-

LHS:-

sec 2A = Sec 2(39)= sec78°

RHS:-

cosec (A – 27°)

=>Cosec (39°-27)

=>Cosec12°

=>Cosec (90-78°)

Sec78°

LHS=RHS

Used formula:-

• Sec(90°-A)=Cosec A
• Cosec A =Sec (90°-A)