Advertisements
Advertisements
Question
Find the value of tan `(7pi)/12`
Solution
tan `(7pi)/12 = 7 xx 180/12`
= 7 × 15°
= 105°
tan(105°) = tan(90° + 15°)
= – cot 15°
= `- 1/tan15^circ`
= `- 1/(tan(45^circ - 30^circ))`
= `- 1/((tan45^circ - tan30^circ)/(1 + tan45^circ* tan30^circ))`
= `- (1 + tan45^circ* tan30^circ)/(tan45^circ - tan30^circ)`
= `- (1 + (1) * (1/sqrt(3)))/(1 - 1/sqrt(3))`
= `- ((sqrt(3)+ 1)/sqrt(3))/((sqrt(3) - 1)/sqrt(3))`
= `- (sqrt(3) + 1)/(sqrt(3) - 1)`
= `- (sqrt(3) + 1)/(sqrt(3) - 1) xx - (sqrt(3) + 1)/(sqrt(3) + 1)`
= `- ((sqrt(3) + 1)^2)/((sqrt(3))^2 - 1^2)`
= `- ((3 + 2sqrt(3) + 1))/(3 - 1)`
tan(105°) = `- (4 + 2sqrt(3))/2`
= `- (2 + sqrt(3))`
APPEARS IN
RELATED QUESTIONS
If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Express the following as a sum or difference
sin 4x cos 2x
Express the following as a sum or difference
sin 5θ sin 4θ
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If A + B + C = 180°, prove that `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
