solve the equation secx - cosecx=4/3 - Maths - Trigonometric Functions

Question

solve the equation secx - cosecx=4/3

Ghanshyam Dhakar · Accepted Answer

Dear
student,
secx-cosecx  =431cosx - 1sinx  =43sinx-cosxsinxcosx=43 
1square both side sinx-cosx2sinxcosx2=169sin2x+cos2x-2sinxcosxsinxcosx2=1691-2sinxcosxsinxcosx2=1691sinxcosx2-2sinxcosx-169=0let 1sinxcosx  =yy2-2y-169  = 09y2-18y-16=0y=18±182+4×16×918y = 83,-23then sinxcosx=38,-32put in eq1  sinx -cosx = 12,       sinx -cosx =-2 use asinx-bcosx  = a2+b2sinx-p   where  p =  sin-1ba2+b22sinx-π4 = 12 ,    2sinx-π4 =-2   not possible sinx-π4 = 122x = π4+sin-1122 x = π4+sin-1122 +2nπ   answer sinx-π4 = sinπ-x-π4 = 122x = 5π4-sin-1122 x = 5π4-sin-1122 +2nπ   answer 
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