Sin(x)csc(x)?

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Answer 1 · 2018-03-07T14:58:57

#color(green)(=> 1#

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#sin x * csc x = sin x * (1 / sin x)# using fundamental identities.

#cancel( sin x )* (1 / cancel (sin x) ) = 1#

Answer 2 · 2018-03-07T15:04:58

# \qquad \qquad \qquad \qquad \qquad sin(x) csc(x) \ = \ 1. #

# "Recall the definition of the" \ \ csc \ \ "function": #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad csc(x) \ = \ 1/sin(x). #

# "Thus, at once:" #

# \qquad \qquad \qquad \qquad \quad \ \ sin(x) csc(x) \ = \ sin(x) cdot 1/sin(x) \ = \ 1. #

# "That's it !!" #