Question

Evaluate (1+tanteta + sec teta ) ( 1+cot teta -cosec teta)

Answer 1

Answer:

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Answer 2

Answer:

2

Step-by-step explanation:

(1 + tan θ + sec θ)(1 + cot θ - cosec θ)

=(1 + sin θ/cos θ + 1/cos θ)(1 + cos θ/sin θ - 1/sin θ)

=((cos θ+sin θ +1)/cos θ)((sin θ+cos θ-1)/sinθ)

={((sin θ+cos θ)+1)*((sin θ+cos θ)-1)}/sin θ*cos θ

={(sin θ+cos θ)^2 - 1^2}/sin θ*cos θ

=(sin^2 θ+cos^2 θ+2*sin θ*cos θ-1)/sin θ*cos θ

=(1+2*sin θ*cos θ-1)/sin θ*cos θ

=2*sin θ*cos θ/sin θ*cos θ

=2