Find the value of sin 2-8-sin 2-4

The correct option is C We know nbsp;sin^2π/4 = sin^2 45^∘ = ( 1/√(2))^2 = 1/2 but, we don't know the value of nbsp;sin^2π/8. Using the formula cos2x = 1 ...

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Standard XI

Mathematics

Inequality

Find the valu...

Question

Find the value of $s i n^{2} \frac{π}{8}$ + $s i n^{2} \frac{π}{4}$

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Solution

The correct option is B

We know $s i n^{2} \frac{π}{4}$ = $s i n^{2} 45^{\circ}$ = ${(\frac{1}{\sqrt{2}})}^{2}$ = $\frac{1}{2}$ but, we don't know the value of $s i n^{2} \frac{π}{8}$ .

Using the formula cos2x = 1 - 2 $s i n^{2} x$

$s i n^{2} θ$ = $(\frac{1 - c o s 2 θ}{2})$

$s i n^{2} \frac{π}{8}$ = $\frac{1 - c o s \frac{π}{4}}{2}$ = $\frac{1 - \frac{1}{\sqrt{2}}}{2}$ = $\frac{\sqrt{2} - 1}{2 \sqrt{2}}$

$s i n^{2} \frac{π}{8}$ + $s i n^{2} \frac{π}{8}$

= $\frac{1}{2}$ - $\frac{1}{2 \sqrt{2}}$ + $\frac{1}{2}$ = 1 - $\frac{1}{2 \sqrt{2}}$

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Similar questions

The value of $s i n^{2} (\frac{π}{18}) + s i n^{2} (\frac{π}{9}) + s i n^{2} (\frac{7 π}{18}) + s i n^{2} (\frac{4 π}{9})$ is

Q. The value of

{sin}^{2} \frac{π}{4} + {sin}^{2} \frac{3 π}{4} + {sin}^{2} \frac{5 π}{4} + {sin}^{2} \frac{7 π}{4}

Q. (i) Prove that

s i n^{2} (\frac{π}{8} + \frac{A}{2}) - s i n^{2} (\frac{π}{8} - \frac{A}{2}) = \frac{1}{\sqrt{2}} s i n A

.
(ii) Find the value of

c o s^{2} 45^{o} - s i n^{2} 15^{o}

Q. If

\frac{sin θ}{{sin}^{2} (\frac{π}{8} + \frac{θ}{2}) - {sin}^{2} (\frac{π}{8} - \frac{θ}{2})} = k (θ \neq 2 n π)

, then value of

2 k^{2}

Q. If

L = {sin}^{2} (\frac{π}{16}) - {sin}^{2} (\frac{π}{8})

and

M = {cos}^{2} (\frac{π}{16}) - {sin}^{2} (\frac{π}{8}),

then:

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Find the value of sin2π8 + sin2π4

The correct option is B We know sin2π4 = sin245∘ = (1√2)2 = 12 but, we don't know the value of sin2π8. Using the formula cos2x = 1 - 2 sin2x sin2θ = (1−cos2θ2) sin2π8 = 1−cosπ42 = 1−1√22 = √2−12√2 sin2π8 + sin2π8 = 12 - 12√2 + 12 = 1 - 12√2

Find the value of $s i n^{2} \frac{π}{8}$ + $s i n^{2} \frac{π}{4}$