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Thepotemich [5.8K]
3 years ago
11

Show that the LHS = RHS.

Mathematics
1 answer:
Stolb23 [73]3 years ago
8 0

Step-by-step explanation:

:

  2-csc²A

▬▬▬▬▬▬▬

csc²A + 2cotgA

  2 - 1/sin²A

= ▬▬▬▬▬▬▬▬▬▬

 1/sin²A + 2cosA/sinA

  2sin²A - 1

= ▬▬▬▬▬▬▬

  1 - 2cosAsinA

    sin²A + sin²A - 1

= ▬▬▬▬▬▬▬▬▬▬▬▬

 sin²A - 2cosAsinA + cos²A

  sin²A - cos²A

= ▬▬▬▬▬▬▬

  (sinA - cosA)²

 (sinA - cosA)(cosA + sinA)

= ▬▬▬▬▬▬▬▬▬▬▬▬

   (sinA - cosA)²

 sinA + cosA

= ▬▬▬▬▬▬ <-- Let check "+" and "-"

 sinA - cosA

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