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_(i) =(tan theta)/(cot alpha)rArr cos alpha = (tan theta)/(tan theta_(1))`
`tan theta_(2) = (tan theta)/(cos(90- alpha))`
`tan theta_(1) = (tan theta)/(sin alpha) rArr sin alpha = (tan theta)/(tan theta_(2))`
`sin^(2)mu cos^(2)alpha =1` identify in trignometry
`(tan^(2) theta)/(tan^(2) theta_(2)) + (tan^(2)theta)/(tan^(2) theta_(1))=1`
`tan^(2) theta [1/(tan^(2) theta_(1)) + 1/(tan^(2) theta_(1))]=1`
`cot^(2) theta_(2) + cot^(2) theta_(1) = cot^(2) theta`