Question

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = 

A. 0 

B. 1 

C. 1 

D. −1

Answer 1

To find: (1 + tan θ + sec θ) (1 + cot θ − cosec θ) 

Consider (1 + tan θ + sec θ) (1 + cot θ − cosec θ)

= \(\frac{(sinθ+cosθ)^2-1}{sinθcosθ}\) [∵ (a – b) (a + b) = a² – b²]

= \(\frac{sin^2θ+cos^2θ+2sinθcosθ-1}{sinθcosθ}\)

= \(\frac{1+2sinθcosθ-1}{sinθcosθ}\) [∵ sin²θ + cos²θ = 1]

= \(\frac{2sinθcosθ}{sinθcosθ}\) = 2