1. If sin(50 - 3x/2) = cos(3x - 50) then find the value of tanx.secx.sinx - cotx.sinx.cosx
2. If cotA = 3 - 1/12A then find cotA+cosecA = 6x or -1/6.
3. Find the quadratic polynomial whose zeroes are √3+√5 and √5 - √3.
4. Government of India allotted relief fund to help the families whose houses and shops were ruined in a storm. The fund is represented by 6x³-11x²+15x-24. The fund is equally divided between each of the families of that accident. Each family receives an amount of 3x-7. After distribution 7x+11 amount is left. The DC decided to use this amount to develop infrastructure of the area. Find the number of families which received relief fund from government.
5. Find the diagonals of a square length of whose sides is 8cm.
6. Prove that (1+cotA - cosecA)(1+tanA+secA) = 2.
7. Find the value of k if x³ - 4x²+5x -k is completely divisible by x - 4.
