Question

Prove that tan7.5° = √6 - √3 + √2 - 2

Answer 1

Step-by-step explanation:

How is the value of tan 7.5 equal to √6 - √3 + √2 - 2?

tan15°=tan(60–45)=(tan60-tan45)/(1+tan60.tan45)

tan15°=(√3–1)/(√3+1)

tan 15°= (2.tan 15°/2)/(1-tan^2. 15°/2)

(√3–1)/(√3+1)=(2.tan 15°/2)/(1-tan^2. 15°/2)

2.(√3+1).tan 15°/2=(√3–1)-(√3–1).tan^2. 15°/2

or. (√3–1).tan^2. 15°/2. +2.(√3+1).tan 15°/2 -(√3–1) = 0

or. tan 15°/2=[ -2.(√3+1)+/-√{4.(√3+1)^2+4(√3–1)^2}]/2.(√3–1)

or. tan 7.5°=2[-(√3+1)+/-√{8}]/2.(√3–1)

or. tan7.5°=[-(√3+1)+/-2√2]/(√3–1)

or. tan7.5°=[-√3–1+2√2]/(√3–1). or. [-√3–1–2√2]/(√3–1). (not possible)

or. tan7.5°=(-√3–1+2√2)×(√3+1)/(√3–1)(√3+1)

or. tan7.5°=(-3-√3+2√6-√3–1+2√2)/(3–1)

or tan7.5=(-4–2√3+2√6+2√2)/2

or. tan7.5°=-2-√3+√6+√2

or. tan7.5°= √6-√3+√2–2. Proved.