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. `cot^2theta=cot^2theta_1+cot^2theta_2`
B. `tan^2theta=tan^2theta_1+tan^2theta_2`
C. `cot^2theta=cot^2theta_1-cot^2theta_2`
D. `tan^2theta=tan^2theta_1-tan^2theta_2`

Explanation

Here, `tan theta_1=(V)/(H_1)`
and `tan theta_2=(V)/(H_2)`
and `tan theta=V/H`
`:. H_1=V cot theta_1, H_2=Vcot theta_2, H=Vcot theta`
As `H^2=H_1^2+H_2^2`
`:. V^2cot^2theta=V^2cot^2theta_1+V^2cot^2theta_2`
Hence `cot^2theta=cot^2theta_1+cot^2theta_2`