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Q.

If ϕ1 and ϕ2 be the angles of dip observed in two vertical planes at right angles to each other and ϕ be the true angle of dip, then

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a

cos2ϕ=cos2ϕ1+cos2ϕ2

b

sec2ϕ=sec2ϕ1+sec2ϕ2

c

tan2ϕ=tan2ϕ1+tan2ϕ2

d

cot2ϕ=cot2ϕ1+cot2ϕ2

answer is D.

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Detailed Solution

tan ϕ1=tan ϕcos θ ; cos θ=tan ϕtan ϕ1cos90-θ=sin θ=tan ϕtan ϕ2sin2 θ+cos2 θ=1=tan2 ϕcot2 ϕ1+cot2 ϕ2cot2 ϕ=cot2 ϕ1+cot2 ϕ2
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