Question

Solve the equation on the interval [0, 21). Write numbers as integers or simplified fractions and separate multiple answers with commas. 2 sin’x+ 2 sinx-2=0 The solution set is 8

Answer 1

ut some basic fact sino es positive in 1st and 2nd quadrant: sino [-] of [0,27] Range of when So i.e Sint-A) sin(3) tra sin (1-0) = sino sinca sin (4) Roots of quad is atic equation ax24 62+c = o. given by -b I ſ62-49c st are 2 a question Now From Given equation is 2 sinea + V2 sinx -2 = 0 suppose to sina 2+² +12t 2-0 Za -52 I (52)2 - 4X2X-2 -V2 + vis 2x2 t=-12 I 352 4 4 + t = -12 + 3V2 and to-V2.-312 4 => t = 272 and ta 42 4 x sinx=trz - t = 1 and t = -2 V2 But to sinx Hence fiz and sinaa-r2 but sina =-62 is not possible since Range of sina [1,1] i sina = 152 Here sina is positive sina in in 1st and 2nd quad 79017, so we will get the solution, it must lies in 1st and and quadrant sina=1 te as we know that sin (31) = sin(A) = 1/2 where T ? 22 . Answer c positive Hence, na 2.) 3T 2 4 CS Scanned with CamScanner