Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of cos(x − y)
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
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 `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
Prove that `sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2` = sin 2θ sin 5θ
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 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
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
