If a right-angled triangle XYZ right-angled at Y. If XY = 2 6 and XZ - YZ = 2, then secX + tanX is?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& XZ-YZ=2\\ & h-P=2........\text{(i)}\\ & h^2=(2\sqrt{6}{)}^2+P^2\\ & h^2-P^2={\left(2\sqrt{6}\right)}^2\\ & (h-P)(h+P)=4\times 6\\ & (2)(h+P)=24\\ & h+P=12..........\text{(ii)}\\ & \text{Adding eq }\left(\text{i}\right)\text{ and }\left(\text{ii}\right)\\ & 2h=14\\ & h=7\text{and }P=5\\ & \therefore secX+tanX\\ & =\frac{h}{XY}+\frac{P}{XY}\\ & =\frac{7}{2\sqrt{6}}+\frac{5}{2\sqrt{6}}\\ & =\frac{12}{2\sqrt{6}}\\ & =\frac{6}{\sqrt{6}}\\ & =\sqrt{6}\end{array}$$