Multiple choice

If $\sec 5A = \text{cosec} (A - 30)$, where $\angle A$ is acute angle, then $\angle A =$ ____

  1. $35^{\circ}$
  2. $25^{\circ}$
  3. $20^{\circ}$
  4. $27^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

sec(5A) = cosec(A - 30) implies sec(5A) = sec(90 - (A - 30)). So 5A = 90 - A + 30. 6A = 120. A = 20 degrees.

AI explanation

Using the cofunction identity, secant and cosecant are complementary, so we can write sec 5A equals sec(90 minus (A minus 30)). Setting the arguments equal gives 5A equals 90 minus A plus 30, which simplifies to 6A equals 120. Dividing by 6 gives A equals 20 degrees.

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