Q6 of 61 Page 204

If sinθ, cosθ and tanθ are in G.P., then prove that cot6θ – cot2θ = 1.

Given: sinθ, cosθ, tanθ are in G.P.


So,


cos2θ =sinθ × tanθ


cos2θ =sinθ ×


cos2θ =


Or,


⇒ cot2θ =secθ (1)


Taking LHS= cot6θ –cot2θ


= (cot2θ) 3 – cot2θ


=sec3θ – secθ [Substituting from eqn. (1)]


=secθ (sec2θ -1)


=secθ (tan2θ)


=cot2θ.tan2θ [Substituting from eqn. (1)]


=1


=RHS


Hence proved.


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