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 values of sin(480°)
Find the values of sin (– 1110°)
Find the values of tan(1050°)
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:
tan θ = −2, θ lies in the II quadrant
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)
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 sin(A + B) sin(A – B) = sin2A – sin2B
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Express the following as a sum or difference
cos 5θ cos 2θ
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
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 sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos 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 `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
