Prove that sin θ ( 1 – tan θ ) − cos θ ( 1 − cot θ ) = cosec θ − sec θ

1 thought on “Prove that sin θ ( 1 – tan θ ) − cos θ ( 1 − cot θ ) = cosec θ − sec θ”

1. Step-by-step explanation:

   sinθ(1+tanθ)+cosθ(1+cotθ)

   =sinθ+

   cosθ

   sin

   2

   θ

   +cosθ+

   sinθ

   cos

   2

   θ

   =sinθ+

   sinθ

   cos

   2

   θ

   +

   cosθ

   sin

   2

   θ

   +cosθ

   A=

   sinθ

   sin

   2

   θ+cos

   2

   θ

   +

   cosθ

   sin

   2

   θ+cos

   2

   θ

   As,sin

   2

   θ+cos

   2

   θ=1

   A=

   sinθ

   1

   +

   cosθ

   1

   = cosecθ+secθ

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