Advertisements
Advertisements
प्रश्न
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
Advertisements
उत्तर
tan x = `"n"/("n" + 1)`, tan y = `1/(2"n" + 1)`
tan(x + y) = `(tanx + tany)/(1 - tanx tany)`
= `("n"/("n" + 1) + 1/(2"n" + 1))/(1 - "n"/("n" + 1) * 1/(2"n" + 1))`
= `(("n"(2"n" + 1) + "n" + 1)/(("n" + 1)(2"n" + 1)))/((("n" + 1)(2"n" + 1) - "n")/(("n" + 1)(2"n" + 1))`
= `("n"(2"n" + 1) + "n" + 1)/(("n" + 1)(2"n" + 1) - "n")`
= `(2"n"^2 + "n" + "n" + 1)/(2"n"^2 + "n" + 2"n" + 1 - "n")`
= `(2"n"^2 + 2"n" + 1)/(2"n"^2 + 2"n" + 1)`
tan(x + y) = 1
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
Find the values of sin (– 1110°)
Find the values of cot(660°)
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2` find the value of sin(x + y)
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)
Show that tan 75° + cot 75° = 4
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Express the following as a sum or difference
sin 4x cos 2x
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos 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 = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
