MATH SOLVE

4 months ago

Q:
# Prove csc (pi/2 - x) = sec x

Accepted Solution

A:

Answer:The answer is the last one ⇒ [tex]csc(\frac{\pi }{2}-x)=\frac{1}{sin\frac{\pi }{2}cosx-cos\frac{\pi }{2}sinx }[/tex]Step-by-step explanation:∵ sin(π/2 - x) = sinπ/2 cosx - cosπ/2 sinx∵ sin(π/2) = 1 , ∵ cos(π/2) = 0∴ sin(π/2 - x) = (1) × cosx - (0) sinx = cosx∵ csc(π/2 - x) = [tex]\frac{1}{sin\frac{\pi }{2}-x }[/tex]∴ csc(π/2 - x) = 1/cosx = secx