Question

if cosA = 3/5 and sinB = 5/13 , then the value of TanA + TanB /1-tanA tanB is ​

Answer 1

Answer:

$\frac{63}{16}$

Or

3.9375

Step-by-step explanation:

cosA = 3/5

sin B = 5/13

cos^2A + sin^2A = 1

sin 2A = 1 - (9/25)

sin^2A = 16/25

sinA = +4/5 or -4/5 =

But SinA = +4/5 (Hence, it is in Quadrant I)

cos^2 B = 1- sin^2 B

cos^2 B = 1 - 25/169

cos^2 B = 144/169

cosB = +12/13 or -12/13

But Cos B = +12/13 (Hence, it is in =

quadrant 1)

(tanA + tanB)/(1 - tanA.tanB)

= [(sinA/cosA) + (sinB/cosB)] - [1 - (sinA/ cosA) x (sinB/cosB)]

= [{(4/5) ÷ (3/5)} + ((5/13) - (12/13)}] / [1 -

{(4/5) (3/5)}

× {{5/13) (12/13)}

= [(4/3) + (5/12)] - [1 - (20/36)] =

= (21/12) - (4/9)

= 189/48 =

= 63/16 or 3.9375

Answer 2

Step-by-step explanation:

☯️Explanation:

First, find tan A and tan B.

Cos A = 3/5 ---》 Sin2 A = 1 - 9/25 = 16/25

Cos A = + (-4/5)

Cos A = 4/5 Because A is an Quadarnt.

Yan A = Sin A / Cos A = (4/5) (5/3) = 4/3

Sin B = 5/3---》 Cos2 B = 1 - 25/169 = 144/169

Sin B = +(-12/13)

Sin B = 12/13 Because B is Quadarnt.

Tan B = Sin B/Cos B = (5/13) (13/12) = 5/12

=》APLY THIS TRIG IDENTITY :

Tan (A-B)= Tan A - TanB/1-TanA. Tan B

Tan A - Tan B = 4/3 - 5/12 = 11/12

(1 - Tan A. Tan B) = 1 - 20/36 = 16/36 = 4/9

(Tan A-B) = (11/12) (9/4) = 33/16

⭐33/16(Ans)