1.

To prove:cot A/(cosec A+1) + (cosec A +1)/cot A = 2 sec A​

Answer»

ANSWER :

  • \frac{cotA}{cscA+1}+\frac{cscA+1}{cotA}=2secA

Step-by-step EXPLANATION :

L.H.S

\frac{\frac{cosA}{sinA} }{\frac{1}{sinA}+1 }+\frac{\frac{1}{sinA}+1 }{\frac{cosA}{sinA} }\\\\ =>\frac{\frac{cosA}{sinA} }{\frac{1+sinA}{sinA} }+\frac{\frac{1+sinA}{sinA} }{\frac{cosA}{sinA} }\\\\ =>\frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\\\ =>\frac{cos^2A+(1+sinA)^2}{(1+sinA).cosA}\\\\ =>\frac{cos^2A+1+sin^2A+2sinA}{(1+sinA).cosA}\\\\ =>\frac{1+1+2sinA}{(1+sinA)cosA}\\\\ =>\frac{2(1+sinA)}{(1+sinA)cosA}\\\\ =>\frac{2}{cosA} \\\\=>2secA

R.H.S

Hence PROVED.


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