Question

सिद्ध कीजिए कि √(1 + cos A) /√(1 – cos A) = cosec A + cot A

Answer 1

Answer:

सिद्ध कीजिए कि √(1 + cos A) /√(1 – cos A) = cosec A + cot A

Step-by-step explanation:

√(1 + cos A) /√(1 – cos A) = cosec A + cot A

L.H.S.=

√(1 + cos A) /√(1 – cos A)

=$\sqrt{(1+cosA)/(1-cosA)}$

= $\sqrt{(1+cosA)x(1+cosA)/(1-cosA)x(1+cosA)}$

= $\sqrt{(1+cosA)^{2}/1^{2}-cos^{2}A }$

= $\sqrt{(1+cosA)^{2}/sin^{2}A }$

= $\frac{1+cosA}{sinA}$

=$\frac{1}{sinA}+\frac{cosA}{sinA}$

= cosecA + cotA

= R.H.S

Therefore, √(1 + cos A) /√(1 – cos A) = cosec A + cot A