Question

I want the prove if anyon knows plzz tell us !

Jai Jagannath​

Answer 1

Correct Question :--- if asin@ + bcos@ = c, prove that ,

acos@ - bsin@ = ±√(a² + b² - c²) ....

Solution :----

→ asin@ + bcos@ = c

Squaring both sides and using (a+b)² = a² + b² + 2ab we get,

→ (asin@ +bcos@)² = c²

→ a²sin²@+b²cos²@+2absin@cos@ = c²

Now, putting sin²@ = (1-cos²@ and cos²@ = 1-sin²@ we get ) .

→ a²(1-cos²@)+b² (1-sin²@)+2absin@cos@ = c²

→a²-a²cos²@+b²-b²sin²@+2absin@cos@ = c²

→a² + b² - c² = a²cos²@ + b²sin²@ - 2absin@cos@

[ using a² + b² - 2ab = (a-b)² in RHS now ]

→a² + b² - c² = (acos@ - bsin@)²

[ Square root now both sides we get,

→ (acos@ - bsin@) = ±√(a² + b² - c²)

Hence, Proved ......