Question

15. (1 + coto - coseco) (1 + tano + seco) = 2 prove​

Answer 1

Answer:

(1+cotθ-cscθ)(1+tanθ+secθ) =

1 + tanθ + secθ + cotθ + 1 + cotθsecθ - cscθ - cscθtanθ - cscθsecθ =

2 + tanθ + secθ + cotθ + (cosθ/sinθ)(1/cosθ) - cscθ - (1/sinθ)(sinθ/cosθ) - (1/sinθ)(1/cosθ) =

2 + tanθ + secθ + cotθ + cscθ - cscθ - secθ - (1/sinθ)(1/cosθ) =

2 + tanθ + cotθ - (1/sinθ)(1/cosθ) =

2 + sinθ/cosθ + cosθ/sinθ - (1/sinθ)(1/cosθ) =

2 + (sin²θ + cos²θ - 1) / (sinθcosθ) =

2 + (1-1) / (sinθcosθ) =

2 + 0 =

2