Question

7. if tanA = 4/3, find cosA​

Answer 1

Solution:

$\sf{tanA = \dfrac{4}{3}}\\\\\\\Rightarrow \sf{\dfrac{Opposite \: side}{Adjacent \:side} = \dfrac{4}{3}}\\\\\\\to \sf{Opposite \: side = 4}\\\sf{Adjacent \: side = 3}$

Now, By Pythagoras theorem,

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

→ (Hypotenuse)² = 4² + 3²

→ (Hypotenuse)² = 16 + 9

→ (Hypotenuse)² = 25

→ Hypotenuse = √25

→ Hypotenuse = ± 5

Side cannot be negative.

So, Hypotenuse = 5

$\sf{cos A = \dfrac{Adjacent \: side}{Hypotenuse}}\\\\\\\therefore \boxed{\bf{cos A = \dfrac{3}{5}}}$

Know more:

• sin is a trigonometric ratio which means opposite side divided by hypotenuse. Its inverse is cosec

• cos is a trigonometric ratio which means adjacent side divided by hypotenuse. Its inverse is sec
• tan is a trigonometric ratio which means Opposite side divided by Hypotenuse. Its inverse is cot