Question

you guys plz help me .....

very urgent ...
if u cannot answer plz don't reply ....
thanks​

Answer 1

Answer:

Step-by-step explanation:

A)

According to trigonometric properties,

Sin θ = 4/5.

But we know that Sin θ = P/H

Perpendicular = 4, Hypotenuse = 5.

Applying Pythagoras theorem,

Base² =  Hypotenuse² - Perpendicular²

           = 25 - 16 = 9

Base = 3.

Thus we know that

=> Cos θ = B/H= 3/5

=> Tanθ = P/B = 4/3

=> Cotθ = B/P = 3/4

=> Sec θ = H/B = 5/3

Now substitute the values in the equation 4 Tan θ  - 5 Cosθ / Secθ + 4 Cotθ

= [4 (4/3) - 5 (3/5)] / [5/3 + 4 (3/4)]

= [16/3 - 3] / [5/3 + 3]

= [7/3] / [14/3] = 7/14 = 1/2.    

B)

5Tan θ = 4

=> Tanθ = 4/5 =  P/B

Perpendicular = 4, Base = 5.

Applying Pythagoras theorem,

Hypotenuse²  = Base²  + Perpendicular²

                        = 25 + 16 = 41.

Hypotenuse = √41.

=> Sinθ = P/H =  4/√41

=> Cos θ = 5/√41

Substituting the values in 5 SInθ - 3 Cosθ / 5SInθ + 2 Cosθ

= [5 (4/√41) - 3(5/√41)] /  [5 (4/√41) + 2(5/√41)]

= [5/√41] / [30/√41]

= 5/30 = 1/6