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Trigonometric Ratios of Allied Angles

range of sec^...

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range of sec^2x-†an x+1/(sec^2x+†an x+1

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Q. Range of the function

f (x) = \frac{s e c^{2} x - t a n x}{s e c^{2} x + t a n x} - \frac{π}{2} < x < \frac{π}{2}

1 + 2 c o s e c x = - \frac{s e c^{2} (x / 2)}{2}

Show that Sec²x - tan⁶x= 1 +3sec²x tan²x

Q. General solution of

\frac{1 - {t a n}^{2} x}{{s e c}^{2} x} = \frac{1}{2}

{lim}_{x \to \frac{π}{4}} \frac{{s e c}^{2} x - 2}{t a n x - 1}

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