Question

Find the value of tan(55°-A)-cot(35°+A)

Answer 1

tan(55-A)-cot(35+A)

cot(90-55+A)-cot(35+A)

cot(35+A)-cot(35+A)

0

Answer 2

The value of $\tan (55^{\circ}-A)-\cot (35^{\circ}+A)$ is 0.

The value of $\tan (55^{\circ}-A)-\cot (35^{\circ}+A)$ can be found using the formula of allied angles.  

To solve this, we have to make the trigonometric functions common  

$\tan (55^{\circ}-A)-\cot (35^{\circ}+A)$

The formula of allied angles to convert tan into cot is  

$\tan (90^{\circ}-\theta)=\cot \theta$

Now, find the number which give $55^{\circ}$ while subtracting with $90^{\circ}$

$=\tan (90^{\circ}-35^{\circ}-A)-\cot (35^{\circ}+A)$

Taking minus sign common in the first term

$=\tan (90^{\circ}-(35^{\circ}+A))-\cot (35^{\circ}+A)$

From this the first term it is observed that it is suitable for the formula $\tan (90^{\circ}-\theta)=\cot \theta$

Therefore, in the place of $\tan (90^{\circ}-(35^{\circ}+A)=\cot (35^{\circ}+A)$

$=\cot (35^{\circ}+A)-\cot (35^{\circ}+A)$

= 0.