1、两角和与差的正弦、余弦和正切公式第四课时 练习1.若sin =35,则cos 2=(). A.-725 B.725 C.1625 D.9252.若tan +1tan=4,则sin 2=().A.15 B.14 C.13 D.123.化简tan141-tan214cos 28的结果为().A.sin282 B.sin 28C.2sin 28 D.sin 14cos 284.已知-2,2,且2cos 2+15sin +2=0,则tan =().A.-1515 B.1515 C.-15 D.155.(多选题)下列各式中,值为12的是().A.tan22.51-tan222.5 B.tan 15cos
2、215C.33cos212-33sin212 D.tan301-tan2306.已知-4,4,tan2-4=17,则tan =.7.已知cos4-sin4=23,且0,2,则sin 2=,cos2+3=.8.(多选题)已知cos =35,则1+2cos(2-4)sin(+2)=().A.25 B.75 C.145 D.-259.已知,都是锐角,且cos =1+sintan,则().A.-=4 B.2-=2C.+=2 D.2+=210.已知sin +cos =55,且2,则sin 2=;tan =.11.已知函数f(x)=2cosx-6,xR.(1)求f()的值;(2)若f+23=65,-2,0
3、,求f(2)的值.12.已知sinx2-2cosx2=0.(1)求tan x的值;(2)求cos2xcos54+xsin(+x)的值.参考答案1.B2.D3.A4.A5.AC6.127.532-1568.CD9.B10.-45-211.【解析】(1)f()=2cos-6=-2cos6=-232=-3.(2)因为f+23=2cos+23-6=2cos+2=-2sin =65,所以sin =-35.又-2,0,故cos =1-sin2=1-352=45,所以sin 2=2sin cos =2-3545=-2425,cos 2=2cos2-1=2452-1=725.所以f(2)=2cos2-6=2cos 2cos6+2sin 2sin6=272532+2-242512=73-2425.12.【解析】(1)由sinx2-2cosx2=0知,cosx20,所以tanx2=2,所以tan x=2tanx21-tan2x2=221-22=-43.(2)由(1)知tan x=-43,所以cos2xcos54+xsin(+x)=cos2x-cos4+x(-sinx)=cos2x-sin2x22cosx-22sinxsinx=(cosx-sinx)(cosx+sinx)22(cosx-sinx)sinx=2cosx+sinxsinx=21+tanxtanx=24.
