If Sin^ -1+Cos^-1=3 find Sin^ -3+Cos^ -3

Описание: This is a trigonometric question where 1/sin + 1/ cos = 3 is given and we are asked to find the value of 1/sin^3 + 1/cos^3. As we want the cubic identity that is a^3 + b^3 =(a+b)^3 - 3ab(a+b). The value of a+b is given but however we need the value of ab = sin cos. For this we use the identity (a+b)^2 = a^2 + b^2 + 2ab. The use of this identity gives us quadratic equation. But the roots of the quadratic is not a perfect root. This leads us to use the discriminate method of finding the roots of the equation. The answer comes with plus and minus sign. Also we need to rationalise the expression to arrive at a simple answer. This answer is then substituted in the main expression of a^3 + b^3 which is simplified to arrive at the answer. Here we have two answers one expression with a positive sign and the other with a negative sign. Both are the answers to the given question. Written explanation sounds difficult to understand. But I am sure if you watch the video the method and the concept used will be clear and is easy to understand. To solve this we need your basics clear. The identity (a+b)^3, (a+b)^2, root of a quadratic equation by discriminate method then finally rationalising the expression and simplifying the answer so that it looks easy to understand and visualise the answer.