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 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
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`
Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Find the value of cos 105°.
Prove that cos(π + θ) = − cos θ
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(A + B) sin(A – B) = sin2A – sin2B
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Express the following as a sum or difference
sin 4x cos 2x
Express the following as a sum or difference
sin 5θ sin 4θ
Prove that `(sin(4"A" - 2"B") + sin(4"B" - 2"A"))/(cos(4"A" - 2"B") + cos(4"B" - 2"A"))` = tan(A + B)
If A + B + C = 180°, prove that `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
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 sin 2A + sin 2B + sin 2C = 4 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`
