CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Prove that: $$\cfrac{\cos{A}-\sin{A}+1}{\cos{A}+\sin{A}-1}=co\sec{A}+\cot{A}$$


Solution

$$LHS=\dfrac{(\cos A-\sin A)+1}{(\cos A+\sin A)-1}$$

Taking conjugate

$$=\dfrac{(\cos A-\sin A)+1}{(\cos A+\sin A)-1}\times\dfrac{(\cos A+\sin A)+1}{(\cos A+\sin A)+1}$$

$$=\dfrac{\cos^2A-\sin^2A+2\cos A+1}{2\sin A\cos A}$$

$$=\dfrac{\cos^2A-\sin^2A+2\cos A+\sin^2A+\cos^2A}{2\sin A\cos A}$$

On solving, we get

$$=\dfrac{2\cos^2A+2\cos A}{2\sin A\cos A}$$

$$=\dfrac{\cos A+\cos^2A}{\sin A\cos A}$$

$$=\dfrac{\cos A}{\sin A\cos A}+\dfrac{\cos^2A}{\sin A\cos A}$$

$$=\text{cosec}A+\cot A=RHS$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image