Math, asked by nallujeevani, 8 months ago

plzz ans this. very important ​

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Answered by SUMEETLADE
0

Answer:

good I dnot sorry I dear

Answered by AntonyLigin
2

Answer:

2) 4 sin A sin B sin C

Step-by-step explanation:

Given,

A + B + C = 180°

=> A+ B = 180° - C

(sin2A +sin2B) + sin2C = 2sin( \frac{2A + 2B}{2} )cos(\frac{2A  -  2B}{2} ) + 2sinCcosC \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  = 2sin(A  + B)cos(A   -  B) + 2sinCcosC  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  = 2sin(180 {}^{0}  - C  )cos(A   -  B) + 2sinCcosC \\  \:  \:  \:  \:  \:  \: \:  \:  = 2sinCcos(A   -  B) + 2sinCcosC \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  = 2sinC(cos(A   -  B)  + cosC ) \\  = 2sinC(cos(A    +  B)   -  cos(A    +  B) ) \\  = 2sinC(2sinA \: sinB) \\  = 4sinA \: sinB \: sinC

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