Question

1/sectheta-tantheta - 1/costheta = 1/costheta-1/sectheta+tantheta

Answer 1

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.