Question

4tan a=3.evalute 4sin a- cos a+1/4sin a + cos a-1

Answer 1

Answer:

13/11

Step-by-step explanation:

now ATQ,

4 tan = 3

so, tan = 3/4

As we know, in a triangle there are Hypotenuse, base and height

so, Tan  = Perpendicular / base

Tan  = 3/4

Now, according to the pythagoras theorem

Hypotenuse = √3² + 4² = √9+16 = √25 = 5

now we can find:

Sin = Perpendicular / Hypotenuse = 3/5

Cos = Base / Hypotenuse = 4/5

ATQ,

(4sin - cos + 1)/(4sin + cos - 1) 

= (4 × 3/5 - 4/5 + 1)/(4 × 3/5 + 4/5 - 1)   [putting values]

= (12 - 4 + 5)/(12 + 4 - 5) 

= 13/11

PLS MRK AS BRAINLIEST...

Answer 2

Answer:

according to question :-

4tan A = 3

tan a = 3/4

tan a = p/b = 3/4

so perpendicular = 3

and base = 4

now using Pythagoras theorem :-

hypotenuse ^2 = perpendicular ^2 + base ^2

h^2 = 3^2 + 4^2

h^2 = 9+16

h = √25 = 5

so hypotenuse = 5

now sin A = p/h = 3/5

and cos A = b/h = 4/5

now putting values in the question:-

4sin a - cos a + 1 / 4sin a + cos a - 1

4*3/5 - 4/5 + 1 / 4*3/5 + 4/5 - 1

12/5 - 4/5 + 1 / 12/5 + 4/5 - 1

(12-4+1 / 5) / (12+4-5/5)

(9/5) / (11/5)

9/5 * 5/11 = 9/11

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