For x=2and y=3 the angle tan-1(x)+tan-1(y) equals
135°
45°
90°
180°
Explanation of the correct option :
Find the angle tan-1(x)+tan-1(y)
Given that x=2and y=3
As x>1,y>1⇒xy>1
We know that tan-1(x)+tan-1(y)=π+tan-1(x+y)1-xyfor xy>1
Now, put x=2and y=3 we get
tan-1(2)+tan-1(3)=π+tan-1(2+3)1-6=π+tan-15-5=π+tan-1-1=π-π4=3π4=3×180°4=135°
Hence, the correct option is A.
If the angle between the line x=y−12=z−3λ and the plane x+2y+3z=4 is cos−1(√514), then λ equals