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 values of cos(300°)
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
Find the value of sin105°.
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
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 + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Express the following as a sum or difference
sin 35° cos 28°
Express the following as a product
cos 35° – cos 75°
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 A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
