Question

HELP ME
If cosA=4/5 then find the value of
cotA-sinA/2tanA. Plzz Solve in easier method

Answer 1

Answer:

22

45

Step-by-step explanation:

In a triangle ABC, where angle B is right angled,

Given:-

CosA = 4/5.

Now, CosA = Base/Hypotenuse.

Taking angle A as the main angle, now we have AB as 4 and AC as 5.

Now, taking B as the main angle as earlier taken, we'll find BC using Pythagoras Theorem.

Therefore, using Pythagoras theorem, we have

AC^2 = AB^2 + BC^2

=> 5^2 = 4^2 + BC^2

=> 25 = 16 + BC^2

=> 25 - 16 = BC^2

=> 9 = BC^2

=> BC^2 = 9

=> BC = Root over of 9

=> BC = 3.

Now, we've got all the sides of our triangle.

So now, we'll find the values of CotA, SinA and TanA individually.

Now, again taking angle A as the main angle, we have

CotA = Base/ Height

= 4/3.

SinA = Height/Hypotenuse

= 3/5.

TanA = Height/Base

= 3/4.

So now as we have all the values needed for the sum, we now shall start solving it.

CotA - SinA/2TanA

=> 4/3 - 3/5 ÷ 2 × 3/4

=> 4/3 - 3/5 ÷ 3/2 (Cancel 2&4)

=> 20-9/15 ÷ 3/2 ( LCM of 3 and 5)

=> 11/15 ÷ 3/2

=> 11/15 × 2/3

=> 22/45.

Therefore, final answer is 22/45.

Hope you understood it well.

Please mark it as brainliest if you have understood it...