Question

(1 + tan 0 + sec 0) (1 + cot 0 - cosec ) =​

Answer 1

[tex]\bold{\huge{Answer:-} } \\\bold{(1+tanθ+secθ)(1+cotθ-cosecθ)} \\=(1 + \frac{sinθ}{cosθ} + \frac{1}{cosθ} )(1 + \frac{cosθ}{sinθ} - \frac{1}{sinθ} ) \\ = \frac{cosθ + sinθ + 1}{cosθ} \times \frac{sin θ+ cosθ-1 }{sinθ} \\ = \frac{ {(sinθ + cosθ)}^{2} - {(1)}^{2} }{sinθcosθ} \\ = \frac{ {sin}^{2}θ + {cos}^{2}θ + 2sinθcosθ - 1}{sinθcosθ} \\ = \frac{1 - 1 + 2sinθcosθ}{sinθcosθ} \\ = \frac{2sinθcosθ}{sinθcosθ} \\ = 2 \\ \bold{ \large{ \boxed{ (1+tanθ+secθ)(1+cotθ-cosecθ) = 2} } }

[/tex]