if a sin theta + b cos theta is equals to C then prove that A cos theta minus B sin theta is equals to root under a square + b square minus C square
Share
if a sin theta + b cos theta is equals to C then prove that A cos theta minus B sin theta is equals to root under a square + b square minus C square
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
ANSWER
Let θ be an angle such that
... a cos θ + b sin θ = c ............. (1)
Squaring both sides,
... a² cos² θ + b² sin² θ +2ab sin θ cos θ = c²
∴ a² ( 1 - sin² θ ) + b² ( 1 - cos² θ ) +2ab sin θ cos θ = c²
∴ a² - a² sin² θ + b² - b² cos² θ +2ab sin θ cos θ = c²
∴ a² + b² - c² = a² sin² θ + b² cos² θ - 2ab sin θ cos θ
∴ ( √(a²+b²-c²) )² = ( a sin θ - b cos θ )²
∴ a sin θ - b cos θ = ± √(a²+b²-c²)
Hence, Proved
Answer:
Ido you doing today is the only thing I want you doing today is they're not only the baby not only the
Step-by-step explanation:
the door past tense and and sweet dreams my love to you like to you and your family and friends la pan card copy kart aahe ka mobile phone number