Can someone check my answers please? Thank you!
If tan x = 3/5, evaluate:
1) tan 2x
2) tan 3x
==> For #1, I got 15/8; for #2, I got -99/5. Are these answers correct?
both correct, good job
Thank you :)
To check if your answers are correct, we need to use the trigonometric identity for tangent angles, which states that:
tan(2x) = (2tan(x)) / (1 - tan^2(x))
tan(3x) = (3tan(x) - tan^3(x)) / (1 - 3tan^2(x))
Let's substitute the given value of tan(x) = 3/5 into these formulas and simplify to verify your answers:
1) tan(2x) = (2 * (3/5)) / (1 - (3/5)^2)
= (6/5) / (1 - 9/25)
= (6/5) / (16/25)
= (6/5) * (25/16)
= 15/8
Based on your calculations, you correctly evaluated tan(2x) as 15/8.
2) tan(3x) = (3 * (3/5) - (3/5)^3) / (1 - 3 * (3/5)^2)
= (9/5 - 27/125) / (1 - 9/25)
= (9/5 - 27/125) / (16/25)
= ((9/5) * (125/125) - (27/125)) / (16/25)
= ((1125/625) - (27/125)) / (16/25)
= (1125/625 - 27/125) * (25/16)
= (1125*5 - 27*25) / (625*16)
= (5625 - 675) / 10000
= 4950 / 10000
= 99/200
Based on your calculations, you incorrectly evaluated tan(3x) as -99/5, it should be 99/200.
In conclusion, your answer for tan(2x) is correct as 15/8, but your answer for tan(3x) should be 99/200 instead of -99/5.