Question 24

ΔDEF is right angled at E. If m$$\angle$$F = $$30^\circ$$, then ﬁnd the value of $$(cos D - \frac{1}{\sqrt2})$$

Solution

Sum of angles of $$\triangle$$ DEF = $$\angle D+\angle E+\angle F=180^\circ$$

=> $$\angle D+90^\circ+30^\circ=180^\circ$$

=> $$\angle D=180^\circ-120^\circ=60^\circ$$

To find : $$(cos D - \frac{1}{\sqrt2})$$

= $$cos(60^\circ)-\frac{1}{\sqrt2}$$

= $$\frac{1}{2}-\frac{1}{\sqrt2}$$

= $$\frac{(\sqrt{2}-2)}{2\sqrt{2}}$$

=> Ans - (C)

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