Prove that-sin 2-8-A-2-sin 2-8-A-2-1-2sin A

LHS, sin^2 (π/8+A/2 ) sin^2 (π/8 A/2 ) = [sin(π/8 + A/2 )+sin (π/8 A/2 ) ][sin (π/8+A/2 ) sin (π/8 A/2 ) ] [sin π/8. cos A/2+ cos π/8. sin A/2+sin π/8. cos.A ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

Prove that:si...

Question

Prove that:

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

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Solution

LHS,

$s i n^{2} (\frac{π}{8} + \frac{A}{2}) - s i n^{2} (\frac{π}{8} - \frac{A}{2}) = [s i n (\frac{π}{8} + \frac{A}{2}) + s i n (\frac{π}{8} - \frac{A}{2})] [s i n (\frac{π}{8} + \frac{A}{2}) - s i n (\frac{π}{8} - \frac{A}{2})] [s i n \frac{π}{8} . c o s \frac{A}{2} + c o s \frac{π}{8} . s i n \frac{A}{2} + s i n \frac{π}{8} . c o s . \frac{A}{2} - c o s \frac{π}{8} . s i n \frac{A}{2}] = [s i n \frac{π}{8} . c o s \frac{A}{2} + c o s \frac{π}{8} . s i n \frac{A}{2} - s i n \frac{π}{8} . c o s \frac{A}{2} c o s \frac{π}{8} . s i n \frac{A}{2}] = (2 s i n \frac{π}{8} . c o s \frac{A}{2}) (2 c o s \frac{π}{8} . s i n \frac{A}{2}) = (2 s i n \frac{π}{8} . c o s \frac{π}{2}) (2 s i n \frac{A}{8} . c o s \frac{A}{2}) = s i n^{2} . \frac{π}{8} . s i n^{2} . \frac{A}{2} = s i n \frac{π}{4} . s i n A = \frac{1}{\sqrt{2}} s i n A = RHS$

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Similar questions

Prove that:

$s i n^{2} \frac{π}{8} + s i n^{2} \frac{3 π}{8} + s i n^{2} \frac{5 π}{8} + s i n^{2} \frac{7 π}{8} = 2$

Q. Prove that:

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

Find the general solution of the equation.

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. Prove that
sin ²(π/8 + A/2) - sin² (π/8 - A/2) = sin π/4 * sin A

Q. Prove sin2 π/8 + sin2 3π/8 + sin2 5π/8 + sin2 7π/8 = 2

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Prove that: sin2 (π8+A2)−sin2(π8−A2)=1√2 sin A

Prove that:

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