Question

(Sin to the power of 2) 24 degrees - (sin to the power of 2) 6 degrees =( -1 + square root of 5)/8

Answer 1

$$\begin{gathered} \mathrm{LHS}={\sin }^{2}24°-{\sin }^{2}6° \\ =\sin \left(24°+6°\right).\sin \left(24°-6°\right)\left[\mathrm{as},{\sin }^2\mathrm{A}-{\sin }^2\mathrm{B}=\sin \left(\mathrm{A}+\mathrm{B}\right).\sin \left(\mathrm{A}-\mathrm{B}\right)\right] \\ =\sin 30°.\sin 18° \\ =\frac{1}{2}\times \left(\frac{\sqrt{5}-1}{4}\right) \\ =\frac{\sqrt{5}-1}{8} \\ =\mathrm{RHS} \end{gathered}$$