1/sectheta-tantheta - 1/costheta = 1/costheta-1/sectheta+tantheta
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Answer:
Step-by-step explanation:
L.H.S:
1/secθ-tanθ - 1/cosθ
= Cosθ/1-sinθ - 1/Cosθ
= Cos²θ - 1 + Sinθ / Cosθ(1-Sinθ)
= Sinθ - Sin²θ/Cosθ(1-Sinθ)
= Sinθ(1-Sinθ)/Cosθ(1-Sinθ)
= Tanθ
R.H.S:
1/cosθ - 1/secθ+tanθ
= 1/Cosθ - Cosθ/1+sinθ
= 1 + Sinθ - Cos²θ / Cosθ(1+Sinθ)
= Sinθ + Sin²θ/Cosθ(1+Sinθ)
= Sinθ(1+Sinθ)/Cosθ(1+Sinθ)
= Tanθ
L.H.S = R.H.S
Hence proved.
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