***
If a sin thitta+ b cos 0(thitta) = c, then prove that a cos 0 (thitta)- b sin0 (thitta)= plus-minus [whole√a2 + b2 –c2].
Answers
Answered by
3
Answer:
Asinθ + bcosθ = c
taking square both sides,
(asinθ + bcosθ)² = c²
⇒a²sin²θ + b²cos²θ + 2absinθ.cosθ = c² --------(1)
Let acosθ - bsinθ = x
Squaring both sides
(acosθ - bsinθ)² = x²
⇒a²cos²θ + b²sin²θ -2absinθ.cosθ = x² ------(2)
Add equation (1) and (2),
a²sin²θ + b²cos²θ +2abinθ.cosθ + a²cos²θ + b²sin²θ -2absinθ.cosθ = c² + x²
⇒(a² + b²)cos²θ + (a² +b²)sin²θ = c² + x²
⇒(a² + b²)[sin²θ + cos²θ ] = c² + x²
⇒(a² + b²) = c² + x² [∵ sin²x + cos²x = 1 ]
⇒(a² + b² - c²) = x²
Take square root both sides,
\bold{\pm\sqrt{a^2 + b^2 - c^2} =x}
Hence, acosθ - bsinθ = \bold{\sqrt{a^2 + b^2 - c^2}}
hope this will help uhh
Similar questions
Chemistry,
5 months ago
India Languages,
5 months ago
English,
5 months ago
Social Sciences,
11 months ago
Social Sciences,
1 year ago