If-secx-tanx-1-4-find-secx-tanx-

Question Number 6558 by Tawakalitu. last updated on 02/Jul/16

I f s e c x - t a n x = \frac{1}{4}

f i n d s e c x + t a n x

Commented by Tawakalitu. last updated on 02/Jul/16

Answered by Yozzii last updated on 02/Jul/16

s e c x - t a n x = 0.25 \dots \dots . (1)

(1) \times (s e c x + t a n x) : (s e c x - t a n x) (s e c x + t a n x) = 0.25 (s e c x + t a n x)

{s e c}^{2} x - {t a n}^{2} x = 0.25 (s e c x + t a n x)

\Rightarrow s e c x + t a n x = 4 ({s e c}^{2} x - {t a n}^{2} x)

S i n c e 1 = {s e c}^{2} x - {t a n}^{2} x

∴ s e c x + t a n x = 4 \times 1 = 4

Commented by Yozzii last updated on 02/Jul/16

\frac{1}{c o s x} + \frac{s i n x}{c o s x} = 4

1 + s i n x = 4 c o s x

4 c o s x - s i n x = 1

\sqrt{16 + 1} c o s (x + {t a n}^{- 1} \frac{1}{4}) = 1

c o s (x + {t a n}^{- 1} 0.25) = \frac{1}{\sqrt{17}}

x + {t a n}^{- 1} = 2 n π \pm {c o s}^{- 1} \frac{1}{\sqrt{17}}

x = 2 n π \pm {c o s}^{- 1} \frac{1}{\sqrt{17}} - {t a n}^{- 1} \frac{1}{4} (n \in Z)

Commented by Tawakalitu. last updated on 03/Jul/16

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