Question

cosec² 57° - tan² 33° = ? 

(a) 0 

(b) 1 

(c) -1 

(d) 2

Answer 1

correct answer = (b) 1

We have:

(cosec² 57° - tan² 33°) 

= [cosec² (90° − 33°) − tan² 33°] 

= (sec² 33° − tan² 33°) [∵cosec(90° − θ) = sec θ] 

= 1 [∵ sec²θ − tan²θ = 1]