Question

已知cos(a-6分之π)+sina=5分之4倍根号3，则sin(a+6分之7π)等于？

Answer 1

解析：∵cos(a-π/6)+sina
=cosacosπ/6+sinasiπ/6+sina
=√3/2cosa+3/2sina
=√3(1/2cosa+√3/2sina)=√3sin(a+π/6)
=4√3/5
即sin(a+π/6）=4/5
∴sin(a+7π/6)=sin[π+(a+π/6)]=-sin(a+π/6)
=-4/5

Answer 2

cos(a-π/6）+sina=4/5根号3，即是：根号3/2cosa+3/2sina=4/5根号3……一式。
而sin(a+7/6π）=sin(a+1/6π）=-1/2cosa-根号3/2sina，一式各项除以负根号3即可等到答案 ，答案是5/4