Question

25costheta=7
find tantheta+cottheta​

Answer 1

Let ∠ACB be θ

Given:

• 25 cosθ = 7

To find:

tanθ + cotθ = ?

Solution:

$\sf{\Rightarrow \: \dfrac{Adjacent \: side}{Hypotenuse}=\dfrac{7}{25}}$

So,

• Adjacent Side = BC = 7
• Hypotenuse = AC = 25

By Pythagoras theorem,

(Adjacent Side)² + (Opposite side)² = (Hypotenuse)²

  (BC)² + (AB)² = (AC)²

⇒ 7² + (AB)² = (25)²

⇒ 49 + AB² = 625

⇒ AB² = 625 - 49

⇒ AB² = 576

⇒ AB = √576

⇒ AB = 24

For finding tanθ + cotθ

$\implies \sf{tan \theta + cot\theta =\dfrac{AB}{BC}+\dfrac{BC}{AB}}$

$\sf{\to \: tan \theta + cot \theta =\dfrac{24}{7}+\dfrac{7}{24}}$

$\to \: \sf{tan \theta + cot \theta = \dfrac{576+49}{168}}$

$\therefore \boxed{\bf{tan \theta+ cot\theta=\dfrac{625}{168}}}$