If sin1 4/5 cos1 15/17= tan1 2X/1-X2, then x = - Maths - Inverse Trigonometric Functions

Question

If sin1 4/5 cos1 15/17= tan1
2X/1-X2, then x = ?

Anuradha Sharma · Accepted Answer

If your question is, sin-145-cos-11517=tan-12x1-x2Then we know that sin-1x +cos-1x = π2 soπ2-cos-145-cos-11517=tan-12x1-x2π2-cos-145+cos-11517=tan-12x1-x2As we know that cos-1x+cos-1y = cos-1xy-1-x21-y2π2-cos-145×1517-1-4521-15172=tan-12x1-x2π2-cos-11217-92564289=tan-12x1-x2π2-cos-11217-245×17=tan-12x1-x2π2-cos-13685=tan-12x1-x2we know that sin-1x +cos-1x = π2 sosin-13685=tan-12x1-x2We know that sin-1x =tan-1x1-x2 sosin-13685=tan-136851-36852=tan-13677 sotan-13677=tan-12x1-x2or 2x1-x2=367718x2+77x-18=0

x=-77±772-4×18×-1836or x = -4
5 and 0 22

If sin1 4/5 cos1 15/17= tan1 2X/1-X2, then x = ?

If sin¹ 4/5 cos¹ 15/17= tan¹ 2X/1-X², then x = ?