Question

 If sec A + tan A = x, then sec A ​

Answer 1

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Asked on December 20, 2019 by

Akhil Motwani

If secθ+tanθ=x, then secθ=........

ANSWER

We have,

secθ+tanθ=x ……. (1)

(secθ−tanθ)

(secθ+tanθ)(secθ−tanθ)

=x

(secθ−tanθ)

(sec

2

θ−tan

2

θ)

=x

We know that

sec

2

θ−tan

2

θ=1

Therefore,

(secθ−tanθ)

1

=x

secθ−tanθ=

x

1

……. (2)

On adding the equation (1) and (2), we get

2secθ=x+

x

1

2secθ=

x

x

2

+1

secθ=

2x

x

2

+1

Hence, this is the answer.