Question

& 173 cotA= 4, check whether
1 - tan. A
1 + tan A
cos? A-sin A or not.​

Answer 1

Answer:

Given 3 cotA = 4.

              cotA = 4/3. ----------------- (1).

We know that tan theta = 1/cot theta

                        tan A = 1/cotA

                                  = 1/4/3

                                  = 3/4.  --------------- (2)

We know that cosec^2 theta = 1 + cot^2 theta

                                                 = 1 + (4/3)^2

                                                 = 1 + 16/9

                                                 = 25/9.

                            cosec theta = 5/3.    ---------------- (3)

We know that cosec theta = 1/sin theta

                          (5/3) = 1/sin theta

                          5sin theta = 3 

                            sin theta = 3/5   ------------- (4)

We know that cos^2 theta = 1 - sin^2 theta

                                            = 1 - (3/5)^2

                                            = 1 - 9/25

                                            = 25 - 9/25

                                            = 16/25

                               cos A = 4/5.   ------------- (5)

Now, LHS:

.

Now, RHS: (4)&(5)

LHS = RHS.

Hope this helps!

Answer 2

Answer:

Given, 3cotA = 4 => cotA = 4/3

tanA = 1/cotA = 3/4 = perpendicular/base

perpendicular = 3 , base = 4

from Pythagoras theorem,

hypotenuse = √{perpendicular² + base²}

= √{3² + 4²} = √{9 + 16} = 5

then, sinA = perpendicular/hypotenuse = 3/5

cosA = base/hypotenuse = 4/5

now, LHS = (1 - tan²A)/(1 + tan²A)

= [1 - (3/4)²]/[1 + (3/4)²]

= [1 - 9/16]/[1 + 9/16]

= 7/25

and RHS = cos²A - sin²A

= {4/5}² - {3/5}²

= 16/25 - 9/25

= 7/25

here it is clear that LHS = RHS , hence verified

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