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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