Advertisements
Advertisements
Question
Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Advertisements
Solution
sin x = `8/17`, 0 < x < `pi/2`
⇒ Where x is in I quadrant
∴ sin x, cos x are +ve
From ΔABX,
AX = `sqrt(17^2 - 8^2)`
= `sqrt((17 + 8)(17 - 8))`
= `sqrt((25)(9))`
= 5 × 3
= 15
∴ sin x = `8/17` and cos x = `15/17`
cos y = `- 24/25, pi < y < (3pi)/2`
⇒ Where y is in III quadrant
So, sin y and cos y are –ve
From ΔALY,
AL = `sqrt(25^2 - 24^2)`
= `sqrt(49)`
= 7
∴ cos y = `- 24/25` and sin y = `- 7/25`
sin(x – y) = sin x cos y – cos x sin y
= `(8/17)(- 24/25) - (15/17)(- 7/25)`
= `- 192/425 + 105/425`
= `- 87/425`
APPEARS IN
RELATED QUESTIONS
Find the values of `sin (-(11pi)/3)`
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)
Find the value of tan `(7pi)/12`
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
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
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a sum or difference
cos 5θ cos 2θ
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`
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is
