Question

if cot tita =-3/4 and tita is not inthe second quadrant then 5 sin tita+10 cos tita +9sec tita+16cosec tita -4cot tita​

Answer 1

ANSWER:

Given that,

cotθ = -3/4

In the given ∆ABC‍

Let us consider tha angle 'θ' at C

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\put(0,0){\line(1,0){30}}\put(30,0){\line(0,1){40}}\put(0,0){\line(3,4){30}}\put(13,-4){3\ cm}\put(32,17){4\ cm}\put(8,23){5 cm}\put(3,1){ \theta }\end{picture}$

By using Pythagoras theorem

(hypotenuse)² = (side)² + (side)²

AC² = AB² + BC²

AC² = 4² + (-3)²

AC² = 16 + 9

AC² = 25

AC = √25

AC = 5

Now,

θ is not in 2nd quadrant.Since is in 4th quadrant. Except cosθ & secθ all are negative

→ 5(-sinθ) + 10cosθ + 9secθ + 16(-cosecθ) - (-4cotθ)

→ 5(-4/5) + 10×3/5 + 9×5/3 + 16(-5/4) - [4(-3)/4]

→ -4 + 6 + 15 - 20 + 3

→ -24 + 24

→ 0