Question 24

ΔXYZ is right angled at Y. If m∠X = $$45^\circ$$, then ﬁnd the value of $$(cosec Z +\frac{\sqrt{3}}{2})$$.

Solution

Sum of angles of $$\triangle$$ XYZ = $$\angle X+\angle Y+\angle Z=180^\circ$$

=> $$45^\circ+90^\circ+\angle Z=180^\circ$$

=> $$\angle X=180^\circ-135^\circ=45^\circ$$

To find : $$(cosec Z +\frac{\sqrt{3}}{2})$$

= $$cosec(45^\circ)+\frac{\sqrt3}{2}$$

= $$\sqrt2+\frac{\sqrt3}{2}$$

= $$\frac{(2\sqrt{2}+\sqrt{3})}{2}$$

=> Ans - (A)

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