Question 150

If $$cos\ 20^\circ$$= m and $$cos\ 70^\circ$$=n, then the value of $$m^{2}+n^{2}\ is$$

Solution

$$m^{2}+n^{2}$$ = $$cos^{2}\ 20^{\circ} + cos^{2}\ 70^{\circ}$$

$$\Rightarrow cos^{2}\ (90^{\circ} - 20^{\circ}) + cos^{2}\ 70^{\circ}$$

$$\Rightarrow\ sin^{2}\ 70^{\circ}+cos^{2}\ 70^{\circ}$$

$$\Rightarrow$$ 1 ($$\because$$ $$sin^{2}\theta+cos^{2}\theta=1)$$

Hence, option B is the correct answer.

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