Question

(cosecθ − sinθ)(secθ − cosθ)(tanθ + cot θ) is equal 

A. 0 

B. 1 

C. −1 

D. None of these

Answer 1

To find: (cosecθ – sinθ) (secθ – cosθ) (tanθ + cotθ)

∵ cosecθ = \(\frac{1}{sinθ},sec θ=\frac{1}{cos θ},tan θ\) 

= \(\frac{sinθ}{cosθ},cotθ=\frac{cosθ}{sinθ}\)

∴ (cosecθ – sinθ) (secθ – cosθ) (tanθ + cotθ)

Now, as sin²θ + cos²θ = 1

⇒ sin²θ = 1 – cos²θ 

And cos²θ = 1 – sin²θ

Hence the answer is 'B'