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if sin2A=4/5 then sinA=?prove that tanA(1+sec2A)=tan2A

if sin2A=4/5 then sinA=?prove that tanA(1+sec2A)=tan2A

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Grade:11

1 Answers

Sujit Kumar
111 Points
3 years ago
Question 1 : If Sin(2A)=4/5, Sin(A)=?
Solution : 
Sin2A=2SinACosA
CosA=\sqrt{1-Sin^2A}
Sin2A=2SinA\sqrt{1-Sin^2A}
\frac{4}{5}=2SinA\sqrt{1-Sin^2A}
Squaring on both sides
\frac{4}{25}=Sin^2A(1-Sin^2A)
Let \ Sin^2A=x
After multiplying throughout with 25 we get
25x^2-25x+4=0
After solving the quadratic equation we get
x=\frac{4}{5} \ (or) \ \frac{1}{5}
Therefore:
SinA=\frac{2}{\sqrt{5}} \ (or) \ \frac{1}{\sqrt{5}}
 
 

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