Advertisements
Advertisements
प्रश्न
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Advertisements
उत्तर
Let x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)` = k (say)
`"k"/x` = cos θ
`"k"/y = cos (theta + (2pi)/3)`
`"k"/z = cos (theta + (4pi)/3)`
`"k"/x + "k"/y + "k"/z = cos theta + cos(theta + (2pi)/3) + cos(theta + (4pi)/3)`
`"k"/x + "k"/y + "k"/z` = 0
`"k"[(yz + xz + xy)/(xyz)]` = 0
⇒ xy + yz + zx = 0
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
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
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
Find the value of tan `(7pi)/12`
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
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
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Express the following as a product
sin 50° + sin 40°
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
