Sin A/(1+cos A)=(1-cosA)/sin A
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Answer:
olution:
Given ,
LHS = \frac{sinA}{1+cosA}+\frac{1+cosA}{sinA}
= \frac{sin^{2}A+(1+cosA)^{2}}{sinA(1+cosA)}
= \frac{sin^{2}A+1^{2}+2\times 1\times cosA+cos^{2}A}{sinA(1+cosA)}
= \frac{(sin^{2}A+cos^{2}A+1+2cosA)}{sinA(1+cosA)}
/* By Trigonometric identity:
sin²A + cos²A = 1 */
= \frac{1+1+2cosA}{sinA(1+cosA)}
/* Take 2 , common,we get */
= \frac{2(1+cosA)}{sinA(1+cosA)}
After cancellation, we get
= \frac{2}{sinA}
= 2cosecA
= RHS
Therefore,
\frac{sinA}{1+cosA}+\frac{1+cosA}{sinA}
= 2cosecA
Step-by-step explanation:
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