Question

If $\sec 2A=\text{cosec}(A-{42}^{\circ })$ where $2A$ is acute angle, then value of $A$ is

• A. ${44}^{\circ }$
• B. ${22}^{\circ }$
• C. ${21}^{\circ }$
• D. ${66}^{\circ }$

Answer 1

The correct option is A ${44}^{\circ }$

Given, $\sec 2A=cosec(A-{42}^{\circ })$
$[\because \sec \theta =cosec({90}^{\circ }-\theta )]$
$\Rightarrow cosec({90}^{\circ }-2A)=cosec(A-{42}^{\circ })$
$\Rightarrow ({90}^{\circ }-2A)=(A-{42}^{\circ })$
$\Rightarrow {90}^{\circ }+{42}^{\circ }=A+2A$
$\Rightarrow {132}^{\circ }=3A$
$\Rightarrow A={44}^{\circ }$