Question

If sec 2A = cosec (A – 30°), 0° < 2A < 90°, then find the value of Angle A

Answer 1

Answer:

sec 2A = cosec (A -30)

cosec(90-2A)=cosec(A-30)

90-2A=A-30

120=3A

A=40

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Answer 2

The value of Angle A:

Step-by-step explanation:

According to the question we get,

sec2A = cosec(A - 30°)

We know that sec 2A = cosec(90° - 2A)

Therefore we get,

sec2A = cosec(A - 30°)

⇒cosec(90° - 2A) = cosec(A - 30°)

Crossing taking inverse of cosec in both LHS and RHS, we get:

90° - 2A = A - 30°

⇒90 ° + 30° = 2A+A

⇒120° = 3A

⇒ 40° = A

Thus solving we get,

The angle A is 40°