If sin x-cos x-1-5 then the value of cos 2 x

The correct option is B sinx + cosx = 1/5 Squaring both sides, (sinx + cosx)^2 = 1/25 sin^2x + cos^2x + 2sinxcosx = 1/25 1 + sin2x = 1/25 sin2x = 1/25 1 = ...

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Byju's Answer

Standard XI

Mathematics

Basic Trigonometric Identities

If sin x+cos ...

Question

If sinx + cosx = $\frac{1}{5}$ then the value of cos2x

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Solution

The correct options are
A

B

sinx + cosx = $\frac{1}{5}$

Squaring both sides,

$(s i n x + c o s x)^{2}$ = $\frac{1}{25}$

$s i n^{2} x + c o s^{2} x + 2 s i n x c o s x = \frac{1}{25}$

1 + sin2x = $\frac{1}{25}$

sin2x = $\frac{1}{25}$ - 1 = - $\frac{24}{25}$

We know, $c o s^{2} 2 x$ = 1 - $s i n^{2} 2 x$

= 1 - $- {(\frac{24}{25})}^{2}$

= 1 - $\frac{576}{675}$

= $\frac{49}{625}$

cos2x = $\pm$ $\frac{7}{25}$

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If sinx + cosx = $\frac{1}{5}$ then find the value of sinx.cosx.

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If sinx + cosx = 15 then the value of cos2x

The correct options are A B sinx + cosx = 15 Squaring both sides, (sinx+cosx)2 = 125 sin2x+cos2x+2sinxcosx=125 1 + sin2x = 125 sin2x = 125 - 1 = -2425 We know, cos22x = 1 - sin22x = 1 - −(2425)2 = 1 - 576675 = 49625 cos2x = ± 725

If sinx + cosx = $\frac{1}{5}$ then the value of cos2x