In a right triangle $A B C$, right-angled at $A$, if $\sin B=\frac{1}{4}$, then the value of $\sec B

Question

In a right triangle $A B C$, right-angled at $A$, if $\sin B=\frac{1}{4}$, then the value of $\sec B$ is\

Professor PC Thomas Classes · Answer

(d) : Given, $\sin B=\frac{1}{4}$\ $	herefore \quad \cos ^{2} B=1-\sin ^{2} B$\ $\Rightarrow \cos B=\sqrt{1-\frac{1}{16}}=\sqrt{\frac{15}{16}}$\ $\Rightarrow \quad \cos B=\frac{\sqrt{15}}{4}$\ $	herefore \quad \sec B=\frac{1}{\cos B}=\frac{4}{\sqrt{15}}$\