已知sin(A+4⼀派)=(10⼀7根号2,求cosA的值

2025-05-11 15:35:57
推荐回答(2个)
回答1:

cosA=[(A+兀/4)-兀/4)=√2/2·[cos(A+兀/4)+sin(A+兀/4]=√2/2·(√2/10+7√2/10)=√2/2·4√2/5=4/5

回答2:

sin(A+π/4)=√2/2sina+√2/2cosa=7√2/10 sina+cosa=7/5sin^2 a+cos^2 a=149/25+2cos^2 a-14/5cosa=1cosa=3/5或4/5