a,b都是锐角,且cosa=1/5,sin(a+b)=1/3,求cosb

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a,b都是锐角,且cosa=1/5,sin(a+b)=1/3,求cosba,b都是锐角,且cosa=1/5,sin(a+b)=1/3,求cosba,b都是锐角,且cosa=1/5,sin(a+b)=1

a,b都是锐角,且cosa=1/5,sin(a+b)=1/3,求cosb
a,b都是锐角,且cosa=1/5,sin(a+b)=1/3,求cosb

a,b都是锐角,且cosa=1/5,sin(a+b)=1/3,求cosb
a,b都是锐角,
cosa=1/5
sina = √(1-cos^2a) = 2√6/5
sin(a+b)=1/3
sinacosb+cosasinb=1/3
2√6/5cosb+1/5sinb=1/3
6√6cosb+3sinb=5
3sinb=5-6√6cosb
9sin^2b=25-60√6cosb+216cos^2b
9(1-cos^2b)=25-60√6cosb+216cos^2b
225cos^2b-60√6cosb+16 = 0
(15cosb-2√6)^2=8
15cosb=2√6±2√2
cosb = 2(√6±√2)/15

sin(a+b)=sinacosb+cosasinb=2√6/5*cosb+1/5*sinb=1/3
又sin^b+cos^b=1
联解可得cosb