Question

Find all solutions in [0, 2pi).

a) 2tan(2x)=3

b) cos^2x - sin^2x =1

Answer 1

solution! @ 2 tan (2x) = 3 ; [0,25) => fan( 20) = → 223 ton (3) Calculating tan1 (2) asing Calculator, 0.99 28 sad or 56.3099 ( 1 ) ( ) 3 5 6 397 XA - 0.3128 180 2 TV tre ✓ 360 18otak » 2x= 0.3128 T > x= 0.3128 * x 0.1564 € - Tu = 0.15648) here fana is positive, and we know that - tangent is positive ince I and III quadsaut 180 So prin cipd values are x = 0.15647) (in In quadrant) x = T +0.15641X ( in Il- quadrant) az (1 + 0.1564) = { x = 1.1564 KI Hence x = 0.1564 ñ and a=1.15 640 a o cos?sink de ; (0,2x) Cosa p sinh n=1 ? 1-sin²x - sinx = 1 a los r = line 3) 1-2 sinage = 1 3) 1-1 = 2 Gin 28 3 25inze =0 ) Sinx=0 =) sina- i , with multiplicity 2)

-) S/03 - 0 > a= sinllo) 2) n = si sin(0)=0 > /u-olje, enact value is o. 180td goo Now aine function tic the is positive in to o I and a second quadrante so value in Ir quadsand is na 180-0 = 180-0 a n = 180 or/ s t so x=0&a , [0, 20). Note? Hese K is ex Cluded it we include 27 then 'जा १ कामका