Advertisements
Advertisements
Question
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Advertisements
Solution
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
RELATED QUESTIONS
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin(π + θ) = − sin θ.
Find a quadratic equation whose roots are sin 15° and cos 15°
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`
Prove that sin 105° + cos 105° = cos 45°
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
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
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos 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 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 sin2 B + sin2 C = 1
