Advertisements
Advertisements
प्रश्न
Show that tan 75° + cot 75° = 4
Advertisements
उत्तर
tan 75° = tan(45° + 30°)
= `(tan45^circ + tan30^circ)/(1 - tan45^circ tan30^circ)`
= `(1 + 1/sqrt(3))/(1 - 1/sqrt(3))`
= `((sqrt(3) + 1)/sqrt(3))/((sqrt(3) - 1)/sqrt(3))`
= `(sqrt(3) + 1)/(sqrt(3) - 1)`
cot 75° = `1/tan75^circ`
= `(sqrt(3) - 1)/(sqrt(3) + 1)`
So, L.H.S = tan 75° + cot 75°
= `(sqrt(3) + 1)/(sqrt(3) - 1) + (sqrt(3) - 1)/(sqrt(3) + 1)`
= `((sqrt(3) + 1)^2 + (sqrt(3) - 1)^2)/((sqrt(3) - 1)(sqrt(3) + 1)`
= `(3 + 1 + 2sqrt(3) + 3 + 1 - 2sqrt(3))/(sqrt(3)^2 - 1^2)`
= `8/(3 - 1)`
= `8/2`
= 4
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of cos(x − y)
Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Find a quadratic equation whose roots are sin 15° and cos 15°
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
If cos(α – β) + cos(β – γ) + cos(γ – α) = `- 3/2`, then prove that cos α + cos β + cos γ = sin α + sin β + sin γ = 0
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Express the following as a sum or difference
sin 5θ sin 4θ
If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
