If sin–¹x +sin–¹y+sin–¹z=π/2, prove that x²+y²+z²+2xyz=1

Well, when you know hypotenuse and another side thats opposite to missing angle in a right triangle, you can use 'sin' or 'co-secant' ratios : - sin = opposite/hypotenuse co-secant = 1/sin so, there is no difference. co-secant is just reciprocal of sin. you can use either of them. however you will end up using sine ratio most of the time, as most calculators allow u to get the inverse sin easily without changing settings. hope this !