Question

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

Answer 1

Answer:

hey mate . answer=2

Explanation:

(1+cotθ−cosecθ)(1+tanθ+secθ)=(1+cosθsinθ−1sinθ)(1+sinθcosθ+1cosθ)  

=(sinθ+cosθ−1sinθ)(sinθ+cosθ+1cosθ)

=(sinθ+cosθ)2−12sinθcosθ

=sin2θ+cos2θ+2sinθcosθ−1sinθcosθ

=1+2sinθcosθ−1sinθcosθ

=2sinθcosθsinθcosθ

=2

Answer 2

Answer:

(1+cotθ-cosecθ)(1+tanθ+secθ)

As we know.

((Cotθ=cosθ/sinθ

cosecθ=1/sinθ

tanθ=sinθ/cosθ

secθ=1/cosθ)

⃗→ (1+cosθ/sinθ-1/sinθ)(1+sinθ/cosθ +1/cosθ)

⃗→ ((sinθ+cosθ-1)/sinθ)((cosθ +sinθ+1)/cosθ)

Now; multiplying both equation with each other

⃗→ (Sinθcosθ+cosθ^2 -cosθ+sinθ^2+Sinθcosθ-Sinθ+Sinθ+cosθ-1)/Sinθcosθ

⃗→ ((Sinθcosθ+Sinθcosθ)+(cosθ^2+sinθ^2)+(-cosθ+cosθ)+(-Sinθ+Sinθ)-1))/Sinθcosθ

As we know;

( cosθ^2+sinθ^2=1)

⃗→(2Sinθcosθ+1+0+0-1)/Sinθcosθ

⃗→ 2Sinθcosθ+(1-1)/Sinθcosθ

⃗→ 2Sinθcosθ+0/Sinθcosθ

⃗→ 2Sinθcosθ/Sinθcosθ

Sinθcosθ cancel out with eachout

⃗→ 2