# If θ1 and θ2 be the apparent angles of dip observed in two vertical planes at right angles to each other

Q: 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 :

(a) tan2θ = tan2θ1 + tan2θ2

(b) cot2θ = cot2θ1 – cot2θ2

(c) tan2θ = tan2θ1 – tan2θ2

(d) cot2θ = cot2θ1 + cot2θ2

Ans: (d)

Sol: $\large tan\theta_1 = \frac{tan\theta}{cos\alpha}$

$\large cos\alpha = \frac{tan\theta}{tan\theta_1}$ …(i)

$\large tan\theta_2 = \frac{tan\theta}{cos(90-\alpha)}$

$\large tan\theta_2 = \frac{tan\theta}{sin\alpha}$

$\large sin\alpha = \frac{tan\theta}{tan\theta_2}$ …(ii)

$\large sin^2\alpha + cos^2\alpha = 1$

cot2θ = cot2θ1 + cot2θ2

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