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 sin (– 1110°)
`(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
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
Find the value of sin105°.
Prove that sin(π + θ) = − sin θ.
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Prove that sin 105° + cos 105° = cos 45°
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
Express the following as a sum or difference
sin 35° cos 28°
Express the following as a sum or difference
2 sin 10θ cos 2θ
Express the following as a sum or difference
cos 5θ cos 2θ
Express the following as a product
sin 75° sin 35°
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
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 cos2 B + cos2 C = 1
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
