Advertisements
Advertisements
प्रश्न
Prove the following:
`("cosec"(90^circ - x)sin(180^circ - x)cot(360^circ - x))/(sec(180^circ + x)tan(90^circ + x)sin(-x))` = 1
Advertisements
उत्तर
L.H.S. = `("cosec"(90^circ - x)sin(180^circ - x)cot(360^circ - x))/(sec(180^circ + x)tan(90^circ + x)sin(-x))`
= `(secx*sinx*(- cotx))/((-secx)*(-cotx)*(- sinx)`
= `(secx*sinx*cotx)/(secx*cotx*sinx)`
= 1
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the values of:
cos 75°
Find the value of sin 690°.
Find the value of :
sin (495°)
Find the value of :
tan (– 690°)
Prove the following:
`(cos(pi + x) cos(-x))/(sin(pi - x)cos(pi/2 + x))` = cot2x
Prove the following:
`cos((3pi)/2 + x) cos(2pi + x)[cot((3pi)/2 - x) + cot(2pi + x)]` = 1
Prove the following:
sec 840° . cot (– 945°) + sin 600° tan (– 690°) = `3/2`
Prove the following:
`(sin^3(pi + x)sec^2(pi - x)tan(2pi - x))/(cos^2(pi/2 + x)sin(pi - x)"cosec"^2 - x)` = tan3x
Select the correct option from the given alternatives :
Let 0 < A, B < `pi/2` satisfying the equation 3 sin2A + 2 sin2B = 1 and 3 sin 2A − 2 sin 2B = 0 then A + 2B is equal to ______
Prove the following:
tan 20° tan 80° cot 50° = `sqrt(3)`
Prove the following:
cosec 48° + cosec 96° + cosec 192° + cosec 384° = 0
Prove the following:
cos 36° = `(sqrt(5) + 1)/4`
Prove the following:
sin 36° = `(sqrt(10 - 2sqrt(5)))/4`
Prove the following:
tan6° tan42° tan66° tan78° = 1
If a = sin 175°+ cos 175°, then ______.
If θ = `(17π)/3` then, tan θ – cot θ = ______.
`(1 - 2[cos 60^circ - cos 80^circ])/(2 sin 10^circ)` = ______.
The value of `sin((25π)/3)` is ______.
The value of `cos π/8 + cos (3π)/8 + cos (5π)/8 + cos (7π)/8` is ______.
Find the value of `cos ((29 π)/3)`.
If `cosA/3 = cosB/4 = 1/5, - π/2 < A < 0` and `- π/2 < B < 0`, then the value of 2 sin A + 4 sin B is ______.
The value of cos 480° sin 150° + sin 600° cos 390° is ______.
sin2 17.5° + sin2 72.5° is equal to ______.
If tan θ = `1/sqrt(7)`, then `(("cosec"^2θ - sec^2θ))/(("cosec"^2θ + sec^2θ))` is equal to ______.
cos 1° + cos 2° + cos 3° + ... + cos 180° is equal to ______.
In a ΔABC, if ∠A = `π/2`, then cos2 B + cos2 C is equal to ______.
If ΔABC is a right angled at C, then tan A + tan B is equal to ______.
If `sin A - sqrt(6) cos A = sqrt(7) cos A`, then `cos A + sqrt(6) sin A` is equal to ______.
If sin A + sin B + sin C = 3, then cos A + cos B + cos C is equal to ______.
In a ΔPQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then ∠R is equal to ______.
The value of cos (270° + θ) cos (90° – θ) – sin (270° – θ) cos θ is ______.
The value of the expression sin6 θ + cos6 θ + 3 sin2 θ . cos2 θ is ______.
The value of sin 135° cosec 225° tan 150° cot 315° is ______.
The value of sin 150° cos 120° + cos 330° sin 660° is ______.
