Question

Asin theta +Bcos theta =3 and sin theta +Acos theta =4 find value of a^2+b^2
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Answer 1

Step-by-step explanation:

given :

• Asin theta +Bcos theta =3 and sin theta +Acos theta =4 find value of a^2+b^2

to find :

• find value of a^2+b^2

solution :

• → acos+bsin0 = 4

• ⇒asin0 - bcos0 = 3

• → Now, squaring and adding (1) and (2) .. (acos+bsin)² + (asin - bcos0)² = 4² +

• 3²

• ⇒ a'²cos²0 + 2ab.sincos + b²sin²0 + a²sin²0 - 2ab.sin cos0+ b²cos²0 = 16 + 9

• ⇒ a² (sin²0 + cos²0) + b² (sin²0 + cos²0) = 25

• :: a² + b² = 25

• [ sin²x + cos²x = 1]