Question

please solve this with steps​

Answer 1

Hey ,..

The value of tan 245 + tan 335/tan 205 - tan 115 is equal to

Solution: The value of tan 245+tan 335/tan 205-tan 115 is -1.

Explanation:

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

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

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

\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=-1

Therefore, the value of \tan 245+\frac{\tan 335}{\tan 205}-\tan 115 is -1.

Hope it will help.

✨Sai.

Answer 2

Answer:

Option(3)

Step-by-step explanation:

Important formulas:

(i) tan(360° - θ) = -tanθ

(ii) tan(270° - θ) = cotθ

(iii) tan(180° + θ) = tanθ

Now,

$Given:\frac{tan245 + tan335}{tan205-tan115}$

$=\frac{tan(270-25) + tan(360-25)}{tan(180+25)-tan(90+25)}$

$=\frac{cot25 - tan25}{tan25 + cot25}$

∴ tan25 = p and cotθ = (1/tanθ)

$=\frac{\frac{1}{tan25} -tan25}{tan25+\frac{1}{tan25}}$

$=\frac{\frac{1}{p} - p}{p + \frac{1}{p} }$

$=\frac{\frac{1-p^2}{p}}{\frac{p^2+1}{p}}$

$=\boxed{\frac{1-p^2}{1+p^2}}$

Hope it helps!