Question

1 If the
(tan 245 + tan 35)/
(tan 205 + tan115)

(a) p^2-1 / p^2+1
(b) 1+p^2 /1-p^2
(c) 1-p^2 / 1+p^2
(d) 1+p^2 / 1-p^2​

Answer 1

Step-by-step explanation:

olution: The value of \tan 245+\frac{\tan 335}{\tan 205}-\tan 115tan245+

tan205

tan335

−tan115 is -1.

Explanation:

The given expression is \tan 245+\frac{\tan 335}{\tan 205}-\tan 115tan245+

tan205

tan335

−tan115 .

The find the value of above terms, we will use quadrant concepts of trigonometry.

The function tan is positive in first and third quadrant and the function remains the same for angle 180 and 360 degrees. Write the angles in the sum of either 180 or 360 degree.

First find the value of each term individually.

\tan (245)=\tan (180+65)=\tan (65)tan(245)=tan(180+65)=tan(65)

\tan (335)=\tan (360-25)=-\tan (25)tan(335)=tan(360−25)=−tan(25)

\tan (205)=\tan (180+25)=\tan (25)tan(205)=tan(180+25)=tan(25)

\tan (115)=\tan (180-65)=-\tan (65)tan(115)=tan(180−65)=−tan(65)

Put these values in the given expression.

\tan (65)+\frac{(-\tan (25))}{\tan (65)} -\tan (65)=0-1=-1tan(65)+

tan(65)

(−tan(25))

−tan(65)=0−1=−1

Therefore, the value of \tan 245+\frac{\tan 335}{\tan 205}-\tan 115tan245+

tan205

tan335

−tan115 is -1.