Question
Prove that $\frac{\big(\sin^273^\circ+\sin^217\big)}{\big(\cos^228^\circ+\cos^262^\circ\big)}=1.$
✓
Answer
$\frac{\big(\sin^273^\circ+\sin^217^\circ\big)}{\big(\cos^228^\circ+\cos^262^\circ\big)}=1$$\text{LHS}=\frac{\sin^273^\circ+\sin^217^\circ}{\cos^228^\circ+\cos^262^\circ}$
$=\frac{\big[\sin(90^\circ-17^\circ)\big]^2+\sin^217^\circ}{\big[\cos(90^\circ-62^\circ)\big]^2+\cos^262^\circ}$
$=\frac{1}{1}$ $\big[\because\sin^2\theta+\cos^2\theta=1\big]$
$=1=\text{RHS}$
$=\frac{\big[\sin(90^\circ-17^\circ)\big]^2+\sin^217^\circ}{\big[\cos(90^\circ-62^\circ)\big]^2+\cos^262^\circ}$
$=\frac{1}{1}$ $\big[\because\sin^2\theta+\cos^2\theta=1\big]$
$=1=\text{RHS}$
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