root(1+sinA/1-sinA)+root(1-sinA/1+sinA)
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0
Answer:
Solution:
LHS = \sqrt{(\frac{1+sinA}{1-sinA})}+\sqrt{(\frac{1-sinA}{1+sinA})}
(
1−sinA
1+sinA
)
+
(
1+sinA
1−sinA
)
= \frac{\sqrt{(1+sinA)^{2}}+\sqrt{(1-sinA)^{2}}}{\sqrt{(1-sinA)}\cdot\sqrt{(1+sinA)}}
(1−sinA)
⋅
(1+sinA)
(1+sinA)
2
+
(1−sinA)
2
= frac{1+sinA+1-sinA}{\sqrt{1-sin^{2}A}}frac1+sinA+1−sinA
1−sin
2
A
= \frac{2}{\sqrt{cos^{2}A}}
cos
2
A
2
= \frac{2}{cosA}
cosA
2
= 2secA2secA
= RHS
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