Question

If tan (x+y) = 3/4 and tan (x-y) = 8/15;, then show that tan 2x = 77/36

Answer 1

hey dear
➡➡➡tan(x+ y) = 3/4 and tan(x-y)= 8/15 
tan2x = tan[(x+y) + (x-y)} 
= tan(x+y) + tan(x-y)/ 1-tan(x+y) tan(x- y) 
=[ 3/4 + 8/15]/ 1-3/4*8/15 
= [ 45+ 32]/60/ [ 60- 24]/60 
= 77/36 proved...
Hope it help's☺☺

Answer 2

Given:

A trigonometric functions tan(x + y) = 3/4 and tan(x - y) = 8/15.

To Find:

The value of tan2x.

Solution:

The given problem can be solved using the concepts of trigonometry.

1. The values of tan(x+y) and tan(x-y) are 3/4 and 8/15 respectively.

2. According to the concepts of trigonometry,

• Tan(a+b) = (Tana + Tanb)/(1-Tana*Tanb)

3. Using the formula mentioned above the value of tan2x can be found,

=> Tan(2x) = Tan[(x+y)-(x-y)],

=> Tan[(x+y)-(x-y)] = [tan(x+y) + tan(x-y)]/(1 - tan(x+y)*tan(x-y) ).

=> Tan[(x+y)-(x-y)] = [(3/4) + (8/15)]/[(1 - (3/4)(8/15)],

=> Tan[(x+y)-(x-y)] =  [(3/4) + (8/15)]/[3/5],

=> Tan[(x+y)-(x-y)] = (77/60)/(3/5),

=> Tan[(x+y)-(x-y)] = (77x5)/(60x3),

=> Tan2x = Tan[(x+y)-(x-y)] = 77/36.

Therefore, tan2x is 77/36.