Question

The most general solutions of the equation $secx-1=(\sqrt{2}-1)tanx$ are given by

• A. nπ + π/8
• B. 2nπ, 2nπ + π/4
• C. 2nπ
• D. (2n+1) π

Answer 1

The correct option is B

2nπ, 2nπ + π/4

Let 'C' be the point where the cloud is located.

Let 'A' be the point 200 m above the lake.

$In\Delta ABC$

$tan{30}^{\circ }=\frac{h}{x}$

$\frac{1}{\sqrt{3}}=\frac{h}{x}$

$x=h\sqrt{3}.....\left(i\right)$

$In\Delta ABE$

tan ${60}^{\circ }=\frac{400+h}{x}$

$\sqrt{3}=\frac{400+h}{h\sqrt{3}}$

3h = 400 + h

2h = 400

h = 200 m

$\therefore$ the height of cloud above the lake = 200 + 20

= 400 m