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If $θ_{1}, θ_{2}, θ_{3}, ..... θ_{n}$ are in A.P. then $\frac{\sin θ_{1} + \sin θ_{2} + .... + \sin θ_{n}}{\cos θ_{1} + \cos θ_{2} + ... + \cos θ_{n}} =$

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tan(θ1+θn)

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detailed solution

Correct option is C

sinθ1+sinθ2+...+sinθn=sinnβ2sinβ2.sinθ1+θn2cosθ1+cosθ2+...+cosθn=sin(nβ2)sinβ2.cos(θ1+θn2)where β is the common difference of angles

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If θ1,θ2,θ3,.....θn are in A.P. then sinθ1+sinθ2+....+sinθncosθ1+cosθ2+...+cosθn=

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If $θ_{1}, θ_{2}, θ_{3}, ..... θ_{n}$ are in A.P. then $\frac{\sin θ_{1} + \sin θ_{2} + .... + \sin θ_{n}}{\cos θ_{1} + \cos θ_{2} + ... + \cos θ_{n}} =$