If `theta_1` and `theta_2` be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip `theta` is given by

Options

A. `tan^(2) theta=tan^(2) theta_(1)+tan^(2) theta_(2)`
B. `cot^(2) theta=cot^(2) theta_(1)-cot^(2) theta_(2)`
C. `tan^(2) theta=tan^(2) theta_(1)-tan^(2) theta_(2)`
D. `cot^(2) theta=cot^(2) theta_(1)+cot^(2) theta_(2)`

Answer

D

Explanation

`tantheta_(1)=(tantheta)/(cos alpha)`
`implies tan theta_(2)=(tantheta)/(cos(90-alpha))=(tantheta)/(sin alpha)`
`implies sin^(2) alpha+cos^(2) alpha=1`
`implies cot^(2) theta_(2)+cot^(2)theta_(1)=cot^(2) theta`