Question

1/sec theta + tan theta - 1/ cos theta = 1/ cos theta - 1/ sec theta - tan theta prove that​

Answer 1

Answer:

Step-by-step explanation:

1/Secθ + Tanθ - 1/Cosθ = 1/Cosθ - 1/Secθ - Tanθ

L.H.S:

1/Secθ + Tanθ - 1/Cosθ

=> Secθ - Tanθ/(Secθ - Tanθ)(Secθ + Tanθ)   - 1/Cosθ

=> Secθ - Tanθ/Sec²θ - Tan²θ - 1/Cosθ

= 1 - Sinθ/Cos - 1/Cosθ = 1 - Sinθ - 1 /Cosθ = -SInθ/Cosθ = -Tanθ.

R.H.S:

1/Cosθ - 1/Secθ - Tanθ

=> 1/Cosθ - (Secθ + Tanθ)/(Secθ - Tanθ)(Secθ + Tanθ)

=> 1/Cosθ - (Secθ + Tanθ)/Sec²θ - Tan²θ

=> 1/Cosθ - (1 + Sinθ)/Cosθ

=> 1 - 1 - Sinθ/Cosθ

=> - Sinθ /Cosθ = -Tanθ.

Thus L.H.S = R.H.S

Hence Proved.