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(1 + tan θ + sec θ) (1 + cot θ - cosec θ) (A) 0 (B) 1 (C) 2 (D) - 1

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one month ago Anand Kumar Pandey
1372 Points
```							Dear studentOption (C) is correctJustification:(1 + tan θ + sec θ) (1 + cot θ-cosec θ)We know that,tan θ = sin θ/cos θsec θ = 1/ cos θcot θ = cos θ/sin θcosec θ = 1/sin θNow, substitute the above values in the given problem,we get= (1+ sin θ/cos θ+ 1/cos θ) (1 + cos θ/sin θ-1/sin θ)Simplify the above equation,= (cos θ +sin θ+1)/cos θ × (sin θ+cos θ-1)/sin θ= (cos θ+sin θ)^2 -1^2/(cos θ sin θ)= (cos^2 θ + sin^2 θ + 2cos θ sin θ-1)/(cos θ sin θ)= (1+ 2cos θ sin θ-1)/(cos θ sin θ)(Since cos^2 θ + sin^2 θ = 1)= (2cos θ sin θ)/(cos θ sin θ)= 2Therefore, (1 + tan θ + sec θ) (1 + cot θ-cosec θ) =2Thanks
```
one month ago
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