Question

If sec 5A = cosec (A-30${}^o$), then the value of A is ___.

• A. ${10}^o$
• B. ${20}^o$
• C. ${30}^o$
• D. ${15}^o$

Answer 1

The correct option is B ${20}^o$

cosec(90${}^o$ - 5A) = cosec(A - 30${}^o$) (As, sec$\theta$ = cosec(90${}^o$ - $\theta$))

$\Rightarrow$ 90${}^o$ - 5A = A - 30${}^o$

$\Rightarrow$ 6A = 120${}^o$

$\Rightarrow$ A = 20${}^o$