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Question Number 89047 by jagoll last updated on 15/Apr/20

cos x+sin x=(4/5)  5sin x = ?

cosx+sinx=455sinx=?

Commented by john santu last updated on 15/Apr/20

± (√(1−sin^2 x)) = (4/5)−sin x  1−sin^2 x = ((16)/(25)) −(8/5)sin x +sin^2 x  2sin^2 x−(8/5)sin x−(9/(25)) = 0  ⇒sin x = ((((8/5)−((4(√(34)))/5)))/4)  5 sin x = 2−(√(34)) ≈ −3.831

±1sin2x=45sinx1sin2x=162585sinx+sin2x2sin2x85sinx925=0sinx=(854345)45sinx=2343.831

Answered by MJS last updated on 15/Apr/20

t=tan (x/2) ⇔ x=2arctan t  ((1−t^2 )/(t^2 +1))+((2t)/(t^2 +1))=(4/5)  −5t^2 +10t+5=4t^2 +4  t^2 −((10)/9)t−(1/9)=0  t=(5/9)±((√(34))/9)  ⇒ 5sin x =((10t)/(t^2 +1))=2±((√(34))/2)

t=tanx2x=2arctant1t2t2+1+2tt2+1=455t2+10t+5=4t2+4t2109t19=0t=59±3495sinx=10tt2+1=2±342

Commented by john santu last updated on 15/Apr/20

t^2  = ((59 ± 10(√(34)))/(81)) ⇒ t^2 +1 = ((140 ±10(√(34)))/(81))  10t = ((50±10(√(34)))/9)  ((10t)/(t^2 +1)) = ((50±10(√(34)))/9) ×((81)/(140±10(√(34))))  = (((5±(√(34)))×9)/(14±(√(34)))) ?

t2=59±103481t2+1=140±10348110t=50±1034910tt2+1=50±10349×81140±1034=(5±34)×914±34?

Commented by MJS last updated on 15/Apr/20

=9(((5±(√(34)))(14∓(√(34))))/((14±(√(34)))(14∓(√(34)))))=9((36±9(√(34)))/(162))=2±((√(34))/2)

=9(5±34)(1434)(14±34)(1434)=936±934162=2±342

Commented by jagoll last updated on 15/Apr/20

what the correct answer?  i see has 2 answer

whatthecorrectanswer?iseehas2answer

Commented by MJS last updated on 15/Apr/20

sin x +cos x =(4/5) has 2 solutions in [0; 2π[  ⇒ 2 correct answers

sinx+cosx=45has2solutionsin[0;2π[2correctanswers

Commented by jagoll last updated on 15/Apr/20

o. thanks very much sir.

o.thanksverymuchsir.

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