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If tan theta =a/b find the value of cos theta+sintheta/costheta-sin theta |
Answer» 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). |
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