Question

Solve this question: If a cosQ + b sinQ = 12 a sinQ - b cosQ = 5 (Q=theta) then, a^2 + b^2 = ?

Answer 1

acosQ +bsinQ = 12
squaring both sides,

a²cos²Q +b²sin²Q + 2ab cosQ sinQ = 144 _______(1)
and 
asinQ - bcosQ = 5
squaring both sides,

a²sin²Q +b²cos²Q - 2ab cosQ sinQ = 25 ________(2)

adding (1) and (2),
a²(cos²Q +sin²Q) +b²(sin²Q + cos²Q) = 144+25

⇒a² +b² = 169