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Question

If sinA+cos2A=1/2 and cosA+sin2A=1/3, then find the value of sin3A

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Solution

Given, sinA+cos2A=12,cosA+sin2A=13
Squaring and adding
sin2A+sin22A+2sinAcos2A+cos2A+cos22A+2cosAsin2A=14+19
2+2sin3A=1336sin3A=5972

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