Advertisements
Advertisements
Question
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Advertisements
Solution
a cos (x + y) = b cos (x – y)
a [cos x cos y – sin x sin y] = b [cos x cos y + sin x sin y]
a cos x cos y – a sin x sin y = b cos x cos y + b sin x sin y
a cos x cos y – b cos x cos y = a sin x sin y + b sin x sin y
(a – b) cos x cos y = (a + b) sin x sin y
`("a" - "b") cosy/siny = ("a" + "b") sinx/cosx`
(a – b) cot y = (a + b) tan x
(a + b) tan x = (a – b) cot y .
APPEARS IN
RELATED QUESTIONS
Find the values of cos(300°)
`(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
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Prove that sin 105° + cos 105° = cos 45°
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
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")`
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Express the following as a product
sin 50° + sin 40°
Show that `cos pi/15 cos (2pi)/15 cos (3pi)/15 cos (4pi)/15 cos (5pi)/15 cos (6pi)/15 cos (7pi)/15 = 1/128`
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
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 x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
