Question

if tan theta =a/b find the value of cos theta+sintheta/costheta-sin theta

Answer 1

Answer:-

(Theta is taken as A).

Given:

tan A = a/b

→ Opposite side/Adjacent side = a/b

We know that,

(Hypotenuse)² = (Opposite side)² + (Adjacent side)²

→ (Hypotenuse)² = a² + b²

→ Hypotenuse = √(a² + b²)

→ Cos A = Adjacent side/Hypotenuse

→ Cos A = b/√(a² + b²)

→ Sin A = Opposite side/Hypotenuse

→ Sin A = a/√(a² + b²)

→ (Cos A + Sin A) = (b/√a² + b²) + (a/√a² + b²)

→ Cos A + Sin A = (b + a)/√a² + b²

Similarly,

→ Cos A - Sin A = (b - a)/√a² + b²

Hence,

(Cos A + Sin A)/(Cos A - Sin A) = [(b + a)/

√a² + b² ]/[(b - a)/√a² + b² ]

→ (Cos A + Sin A)/(Cos A - Sin A) = (b + a)/(b - a).