. Find value of following: cot A + tan(180 + A) + tan(90 + A) + tan(360 - A)


Best Answer

Explanation:

Here, 

tan(180 + A) = tan(290 + A)

                        =A, Since the multiple of 90 is even so it remains and the angle 180 + A is in the third quadrant. 

tan(90 + A) = - cotA 

Since multiple of 90 is odd and the angle is in second quadrant and value of  the second is negative. 

tan(360 - A) = tan(4 x 90 – A) = - tanA, since  in fourth quadrant is negative, 

Hence, cotA + tan(180 + A) + tan(90 + A) + tan(360 - A)

          = cotA + tanA – cotA – tanA = 0

Final Answer:

Hence, the value of the expression is, 

cot A + tan(180 + A) + tan(90 + A) + tan(360 - A) = 0

Talk to Our counsellor