Advertisements
Advertisements
प्रश्न
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`
Advertisements
उत्तर
cos x = `- 4/5`
`pi < x < (3pi)/2`
⇒ x is in III quadrant
From ΔPQR,
PQ = `sqrt(5^2 - 4^2)`
= `sqrt(25 - 16)`
= `sqrt(9)`
= 3
Since x is in III quadrant
Both sin x and cos x are negative
∴ sin x = `- 3/5` and cos x = `- 4/5`
sin y = `- 24/25` and y is in III quadrant
Both sin y and cos y are negative
From ΔABC,
BC = `sqrt(25^2 - 24^2)`
= `sqrt(625 - 576)`
= `sqrt(49)`
= 7
So, sin y = `- 24/25` = cos x cos y + sin x si y
= `(- 4/5)(- 7/25) + (-3/5)(- 24/25)`
= `28/125 + 72/125`
= `100/125`
= `4/5`
APPEARS IN
संबंधित प्रश्न
Find the values of `tan ((19pi)/3)`
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I 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
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(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`
Show that tan 75° + cot 75° = 4
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
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)`
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
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
cos 5θ cos 2θ
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
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 sin2 B + sin2 C = 1
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`
Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f4(x) − f6(x) =
