Question

if 4sina+5cosa=3,5sina-4cosa=?

Answer 1

4sina + 5 cosa = 3
take square both sides
16sin²a + 25cos²a +2×4×5sina.cosa = 9 --(1)

again ,

5sina -4cosa = y ( let )

take square both sides

25sin²a + 16cos²a -2×4×5sina.cosa =y²
----(2)

add both eqn

25( sin²a + cos²a) +16( sin²a + cos²a) = y²+ 9

25 + 16 = 9 + y²

32 = y²

y² = 32

y = ±4√2

Answer 2

(4sina+5cosa)²+(5sina-4cosa)=4²+5²

3²+(5sina-4cosa)²=16+25

9+(5sina-4cosa)=41

5sina-4cosa=32