solve for x sin inverse 4x + sin inverse 3x = -pi/2 - Maths - Inverse Trigonometric Functions

Question

solve for x sin inverse 4x + sin inverse 3x = -pi/2

Udbhav Singh · Accepted Answer

Dear Student,

sin-14x+sin-13x=-π2Using, sin-1x+sin-1y=sin-1x1-y2+y1-x2sin-14x1-9x2+3x1-16x2=-π2⇒4x1-9x2+3x1-16x2=sin-π2=-1⇒4x1-9x2+1=-3x1-16x2Squaring both sides, we have⇒4x1-9x2+12=-3x1-16x22⇒16x2(1-9x2)+1+8x1-9x2=9x2(1-16x2)  
using (a+b)2=a2+b2+2ab⇒16x2-144x4+1+8x1-9x2=9x2-144x4⇒8x1-9x2=-7x2-1Squaring both sides, we have⇒8x1-9x22=-7x2+12⇒64x21-9x2=49x4+14x2+1  
using (a+b)2=a2+b2+2ab⇒64x2-576x4=49x4+14x2+1⇒625x4-50x2+1=0
⇒(25x2-1)2=0 
using (a-b)2=a2+b2-2ab⇒25x2-1=0⇒x2=125⇒x=±15

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