Question

a
(d) If tan =
bsino-acos
then the value of
bsin 0+ a cos 0
b
will
be :
1​

Answer 1

Answer:

Given, a cos θ - b sin θ = c  

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)

Step-by-step explanation: