Question

please solve this also trigonometrical ratio​

Answer 1

Answer:

21) given tan x = p/q

to evaluate (p sin x - q cos x)/(p sin x + q cos x)

when tan x = p/q, => perpendicular/base

then hypotenuse = √(p² + q²)

=> sin x = p/√(p² + q²)

=> cos x = q/√(p² + q²)

substitue these values in the given expression,

p sin x = p*p/√(p² + q²) = p²/√(p² + q²)

q cos x = q*q/√(p² + q²) = q²/√(p² + q²)

[p²/√(p²+q²)-q²/√(p²+q²)]/[ p²/√(p²+q²)-q²/√(p²+q²)]

=> (p²-q²)/√(p²+q²) / (p²+q²)/√(p²+q²)

=> (p²- q²)/(p² + q²) => Answer