Question

If $sec\left(4A\right)=cosec(A-20°)$, where $4A$ is an acute angle, then what is the value of $A$?

• A. ${110}^{\circ }$
• B. ${22}^{\circ }$
• C. ${55}^{\circ }$
• D. ${44}^{\circ }$

Answer 1

The correct option is B ${22}^{\circ }$

Given: $sec\left(4A\right)=cosec(A-20°)..\left(i\right)$

$cosec(90°-4A)=cosec(A-{20}^{\circ })..\left(ii\right)(\because secA=cosec({90}^{\circ }-A\left)\right)$

$⟹{90}^{\circ }-4A=A-{20}^{\circ }$

$⟹{90}^{\circ }+{20}^{\circ }=A+4A$

$⟹{110}^{\circ }=5A$

$⟹A={22}^{\circ }$