Advertisements
Advertisements
Question
Find the value of tan 15°.
Advertisements
Solution
tan 15° = tan (45° - 30°)
`= (tan 45^circ - tan 30^circ)/(1 + tan 45^circ tan 30^circ)`
`[because tan ("A - B") = (tan "A" - tan "B")/(1 + tan "A" tan "B")]`
`= (1 - 1/sqrt3)/(1 + 1 (1)/sqrt3)`
`= ((sqrt3- 1)/sqrt3)/((sqrt3 + 1)/sqrt3)`
`= (sqrt3 - 1)/cancel(sqrt3) xx cancel(sqrt3)/(sqrt3 + 1)`
`= (sqrt3 - 1)/(sqrt3 + 1) xx (sqrt3 - 1)/(sqrt3 - 1)`
`= (3 + 1 - 2sqrt3)/(3 - 1)`
`= (4 - 2sqrt3)/2`
`= 2 - sqrt3`
APPEARS IN
RELATED QUESTIONS
Find the value of the following:
cosec 15º
Find the value of the following:
cot 75°
Find the value of the following:
`sin pi/4 cos pi/12 + cos pi/4 sin pi/12`
If cos A = `13/14` and cos B = `1/7` where A, B are acute angles prove that A – B = `pi/3`
Prove that 2 tan 80° = tan 85° – tan 5°.
If cot α = `1/2`, sec β = `(-5)/3`, where π < α < `(3pi)/2 and pi/2` < β < π, find the value of tan(α + β). State the quadrant in which α + β terminates.
Prove that `(sin ("B - C"))/(cos "B" cos "C") + (sin ("C - A"))/(cos "C" cos "A") + (sin ("A - B"))/(cos "A" cos "B")` = 0
If sin α + sin β = a and cos α + cos β = b, then prove that cos(α – β) = `(a^2 + b^2 - 2)/2`
Show that `cos^-1 (12/13) + sin^-1 (3/5) = sin^-1 (56/65)`
The value of sin (-420°)
