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

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