Question : If $\cos 20°= m$ and $\cos 70°=n$, then the value of $m^2+n^2$:
Option 1: $1$
Option 2: $\frac{3}{2}$
Option 3: $\frac{1}{\sqrt2}$
Option 4: $\frac{1}{2}$
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Correct Answer: $1$
Solution :
Given: Let the values of $\cos20°=m$ and $\cos70°=n$
If $A+B=90°$, then $\cos^2 A+\cos^2 B=1$
Here, $70°+20°=90°$
$m^2+n^2= \cos^2\ 20°+\cos^2\ 70°$
$⇒m^2+n^2= 1$
Hence, the correct answer is $1$.
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