Answer:
given in explanation
Step-by-step explanation:
LHS-
=> [tex]\frac{(1+sinA)^2+cos^2A}{cosA(1+sinA)}[/tex]
=> [tex]\frac{1+sin^2A+2sinA+cos^2A}{cosA(1+sinA)}[/tex]
=> [tex]\frac{1+1+2sinA}{cosA(1+sinA)}[/tex]
=> [tex]\frac{2+2sinA}{cosA(1+sinA)}[/tex]
=> [tex]\frac{2(1+sinA)}{cosA(1+sinA)}[/tex]
=> [tex]\frac{2}{cosA}[/tex] => [tex]2secA[/tex] = RHS (Hence, proved)
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Answers & Comments
Answer:
given in explanation
Step-by-step explanation:
LHS-
[tex]\frac{1+sinA}{cosA} + \frac{cosA}{1+sinA}[/tex]
=> [tex]\frac{(1+sinA)^2+cos^2A}{cosA(1+sinA)}[/tex]
=> [tex]\frac{1+sin^2A+2sinA+cos^2A}{cosA(1+sinA)}[/tex]
=> [tex]\frac{1+1+2sinA}{cosA(1+sinA)}[/tex]
=> [tex]\frac{2+2sinA}{cosA(1+sinA)}[/tex]
=> [tex]\frac{2(1+sinA)}{cosA(1+sinA)}[/tex]
=> [tex]\frac{2}{cosA}[/tex] => [tex]2secA[/tex] = RHS (Hence, proved)