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Principal Solution of Trigonometric Equation

Find the valu...

Question

Find the value of ${sin}^{2} 45^{o} - {sin}^{2} 15^{o}$

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Solution

${sin}^{2} 45 - {sin}^{2} 15$
${sin}^{2} A - {sin}^{2} B = sin (A + B) sin (A - B)$
$= sin (45 + 15) sin (45 - 15)$
$= sin (60) sin (30)$
$= \frac{\sqrt{3}}{2} \times \frac{1}{2} = \frac{\sqrt{3}}{4}$

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