Advertisements
Advertisements
Question
Find the value of tan `(7pi)/12`
Advertisements
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
Find the values of sin(480°)
Find the values of cos(300°)
Find the values of tan(1050°)
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Express the following as a sum or difference
cos 5θ cos 2θ
Express the following as a product
sin 75° sin 35°
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
