Question

if 3cot theta =4, show that (1-tan square theta)/(1+tan square theta) = cos square - sin square theta

Answer 1

Hi dear your answer =

3cot Φ = 4
cot Φ = 4/3

then, tanΦ = 3/4. (cotΦ = 1/tanΦ)
1+tan²Φ = sec²Φ
1+(3/4)² = sec²Φ
1+9/16 = sec²Φ
25/16 = sec²Φ
√25/16 = secΦ
5/4 = secΦ

Cos Φ = 4/5. (secΦ= 1/cosΦ)

sin²Φ = 1-cos²Φ
sin²Φ = 1-(4/5)²
sin²Φ = 1-16/25
sin²Φ = 9/25
sinΦ = √9/25
sinΦ = 3/5.

NOW, A. T. Q.
1-tan²Φ/1+tan²Φ = cos²Φ - sin²Φ
1-(3/4)²/1+(3/4)² = (4/5)² - (3/5)²
1-9/16/1+9/16 = 16/25-9/25
7/16/25/16 = 7/25
7/25 =7/25
7/25=7/25. (proved)
i used phi as a place of theta

My dear friend u will understand it.

Have a nice day

Answer 2

Answer:

If not given cos2-sin2

Step-by-step explanation: