Q34 of 35 Page 288

If x = cosecA + cosA and y = cosecA - cosA the prove that

x + y = cosecA + cosA + cosecA - cosA


= 2cosecA


→ sinA = 2/(x + y) = BC/AC


x - y = cosecA + cosA - (cosecA - cosA)


= cosecA + cosA - cosecA + cosA


= 2cosA


Consider the LHS, =


= sin2A + cos2A - 1


= 1 - 1 (∵sin2A + cos2A = 1)


= 0


= RHS


HENCE PROVED


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