If cos- -3-5 - then the value of sin- -1-tan-2tan- is

The correct option is C 3/160 cosα = 35 ∴ tanα= 43 and sinα =45 sinα 1tanα2tanα= 45 342.43=3160 ...

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Standard X

Mathematics

Range of Trigonometric Ratios from 0 to 90 Degrees

If cosα =3/...

Question

If $cos α = \frac{3}{5}$ , then the value of $\frac{sin α - \frac{1}{tan α}}{2 tan α}$ is

\frac{3}{160}

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\frac{841}{160}

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\frac{41}{160}

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\frac{31}{160}

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Solution

The correct option is C $\frac{3}{160}$
$c o s α = \frac{3}{5}$
$∴ t a n α = \frac{4}{3} a n d s i n α = \frac{4}{5}$
$\frac{s i n α - \frac{1}{t a n α}}{2 t a n α} = \frac{\frac{4}{5} - \frac{3}{4}}{2. \frac{4}{3}} = \frac{3}{160}$

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and

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If cosα=35 , then the value of sinα−1tanα2tanα is

The correct option is C 3160cosα=35∴tanα=43andsinα=45sinα−1tanα2tanα=45−342.43=3160

If $cos α = \frac{3}{5}$ , then the value of $\frac{sin α - \frac{1}{tan α}}{2 tan α}$ is

The correct option is C $\frac{3}{160}$
$c o s α = \frac{3}{5}$
$∴ t a n α = \frac{4}{3} a n d s i n α = \frac{4}{5}$
$\frac{s i n α - \frac{1}{t a n α}}{2 t a n α} = \frac{\frac{4}{5} - \frac{3}{4}}{2. \frac{4}{3}} = \frac{3}{160}$