If a is an acute angle and sina -x-1-2 x- find the value tan a-A- -x-1-x-1B- -x-1-x-1C- -x2-1D- -x2-1

The correct option is B √(x 1/x+1)cos^2 a+sin^2a =1 cos^2a =1 x 1/2x=2x x+1/2x=x+1/2x cos a =√(x+1/2x), becuase a is an acute angle. tan a =sin a/cos a=√(x 1/ ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

If a is an ac...

Question

If a is an acute angle and sina = $\sqrt{\frac{x - 1}{2 x}}$ , find the value tan a.

\sqrt{\frac{x - 1}{x + 1}}

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$\sqrt{\frac{x + 1}{x - 1}}$

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$\sqrt{x^{2} - 1}$

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$\sqrt{x^{2} + 1}$

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Solution

The correct option is A $\sqrt{\frac{x - 1}{x + 1}}$
$c o s^{2} a + s i n^{2} a = 1$
$c o s^{2} a = 1 - \frac{x - 1}{2 x} = \frac{2 x - x + 1}{2 x} = \frac{x + 1}{2 x}$
$c o s a = \sqrt{\frac{x + 1}{2 x}}$ , becuase a is an acute angle.
$t a n a = \frac{s i n a}{c o s a} = \sqrt{\frac{x - 1}{x + 1}}$

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If a is an acute angle and sina =√x−12x, find the value tan a.

The correct option is A √x−1x+1cos2a+sin2a=1 cos2a=1−x−12x=2x−x+12x=x+12x cosa=√x+12x, becuase a is an acute angle. tana=sinacosa=√x−1x+1

If a is an acute angle and sina = $\sqrt{\frac{x - 1}{2 x}}$ , find the value tan a.