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Grade 10Trigonometry

1)if a+b=3-cos4 theta and a-b=4sin 2theta then ab is always less than or equal to
options a) 1/2
b)1
c)2/3
d)3 i have corrected the mistake

Profile image of ash jai
12 Years agoGrade 10
Answers icon

1 Answer

Profile image of siddharth gupta
12 Years ago
a+b=3-cos4theta..........(1)
a-b=4sin 2theta............(2)
on squaring and subtracting
a2+b2+2ab -a2-b2+2ab=4ab=9+cos24theta -6cos4theta-16sin22theta
                                        =1+8-16sin22theta+cos24theta-6cos4theta
                                        =1+8(1-2sin22theta)+cos24theta-6cos4theta
                                        =1+8cos4theta+cos24theta-6cos4theta
                                        =(1+cos4theta)2=4ab
                                        i.e ab=(1+cos4theta)2/4
                                        put max. value of cos4theta=1
                                        i.e max. value of ab=(2)2/4=1
WITH REGARDS
SIDDHARTH GUPTA

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