Question

if a cosec theta = b and a cot theta = c , prove that a² + c² = b².​

Answer 1

Answer:

Step-by-step explanation:

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

#Pari Here...

Answer 2

Step-by-step explanation:

it's the correct solution