Question

if secθ =x+1/x, prove that sec θ tanθ =2x or 1/2x.​

Answer 1

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If secθ=x+

4x

1

, prove that secθ+tanθ=2x or

2x

1

Medium

Solution

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secθ=x+

4x

1

⇒sec

2

θ=(x+

4x

1

)

2

⇒1+tan

2

θ=x

2

+

16x

2

1

+

2

1

⇒tan

2

θ=x

2

+

16x

2

1

−

2

1

⇒tan

2

θ=(x−

4x

1

)

2

⇒tanθ=±(x−

4x

1

)

⇒secθ+tanθ=x+

4x

1

+x−

4x

1

=2x

Or secθ+tanθ=x+

4x

1

−x+

4x

1

=

4x

2

=

2x

1