We may classify the NCERT class 10 Trigonometry problems we will solve in this session as elegant within a minute problems, where conventional deductions may take a backseat leaving the lead to pattern and method based high speed problem solving...
After crossing the first barrier in the process of proving a Trigonometric identity, if you go straight ahead without looking at the goal state on the RHS, you might reach a situation where you would have to start again from the goal state expression and backtrack to the simple result you had reached on the first go, not only an awkward solution but also technically an invalid one....
Solve a problem in many ways and apply less facts and more procedures approach, both working towards improving the general problem solving skills of the student.
The conventional approach to math problem solving relies heavily on manipulation of terms using low level mathematical constructs without using the problem solving abilities of the student. Following only this approach to solving problems, students may tend to become used to mechanical and procedural thinking suppressing their inherent creative and innovative out-of-the-box thinking abilities...
The student's intelligence is used for solving the second school math problem in far simpler steps compared to the complex conventional method of solution.
