Question 62

If tan (5x - 10°) = cot (5y + 20°), then the value of x + y is

Solution

Expression : tan (5x - 10°) = cot (5y + 20°)

=> $$tan(5x-10^\circ)=cot[90^\circ-(-5y+70^\circ)]$$

Using, $$cot(90^\circ-\theta)=tan\theta$$

=> $$tan(5x-10^\circ)=tan(-5y+70^\circ)$$

=> $$5x-10^\circ=-5y+70^\circ$$

=> $$5x+5y=70^\circ+10^\circ$$

=> $$5(x+y)=80^\circ$$

=> $$(x+y)=\frac{80^\circ}{5}=16^\circ$$

=> Ans - (B)

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