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Question

If θ1 and θ2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by:
  1. tan2θ=tan2θ1+tan2θ2
  2. cot2θ=cot2θ1+cot2θ2
  3. tan2θ=tan2θ1tan2θ2
  4. cot2θ=cot2θ1cot2θ2

A
tan2θ=tan2θ1tan2θ2
B
cot2θ=cot2θ1+cot2θ2
C
tan2θ=tan2θ1+tan2θ2
D
cot2θ=cot2θ1cot2θ2
Solution
Verified by Toppr

Note that tanθ=VH ...(1)
where θ is true value of dip . Here we assumed θ=
Now, angle of dips, θ1 and θ2 have different formula
tanθ1=VH×cos ...(2)
tanθ2=VH×sin ...(3)
From eqn (1), (2), (3), we can find value of H/V
which cotθ, which when calculate comes option B
cot2θ1+cot2θ2=H2V2(cos2+sin2)=cot2θ
cot2θ=cot2θ1+cot2θ2

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