prove that√2sin10+√3cos35=sin55+2cos65
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Answer:
√2sin10 + √3cos35
= √2 sin(55-45) + √3 cos 35
= √2 (sin55cos45 - cos55sin45) + √3cos(90-55)
= √2 sin55*(1/√2) - √2cos55*(1/√2) + √3sin55
= sin55 - cos55 + √3sin55
= sin55 + √3sin55 - cos55
= sin55 + 2(√3/2*sin55 - 1/2*cos55)
= sin55 + 2(cos30sin55 - sin30cos55)
= sin55 + 2sin(55-30)
= sin55 + 2sin25
= sin55 + 2sin(90-65)
= sin55 + 2cos65
RHS
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