Advertisements
Advertisements
प्रश्न
Prove the following:
sin 20° sin 40° sin 80° = `sqrt(3)/8`
Advertisements
उत्तर
L.H.S. = sin 20° sin 40° sin 80°
= sin 20°. sin 40°. sin 80°
= `1/2(2.sin40^circ.sin20^circ).sin80^circ`
= `1/2[cos(40^circ - 20^circ) - cos(40^circ + 20^circ)].sin80^circ`
= `1/2(cos20^circ - cos60^circ)sin80^circ`
= `1/2cos20^circ.sin80^circ - 1/2 cos60^circ.sin80^circ`
= `1/(2 xx 2)(2sin80^circ.cos20^circ) - 1/2(1/2).sin80^circ`
= `1/4.[sin(80^circ + 20^circ) + sin(80^circ - 20^circ)] - 1/4.sin80^circ`
= `1/4.(sin100^circ + sin60^circ) - 1/4.sin80^circ`
= `1/4sin 100^circ + 1/4sin 60^circ - 1/4sin 80^circ`
= `1/4.sin(180^circ - 80^circ) + 1/4 xx sqrt(3)/2 - 1/4.sin80^circ`
= `1/4sin80^circ + sqrt(3)/8 - 1/4sin80^circ` ...[∵ sin (180° – θ) = sin θ]
= `sqrt(3)/8`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the value of:
sin 15°
Find the values of:
cos 75°
Find the values of:
tan 105°
Find the value of sin 690°.
Find the value of :
cos 315°
Find the value of :
tan 225°
Find the value of :
tan (– 690°)
Find the value of:
sec (–855°)
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 pi/8 = sqrt(2) - 1`
Prove the following:
tan6° tan42° tan66° tan78° = 1
Prove the following:
sin47° + sin61° − sin11° − sin25° = cos7°
`(1 - 2[cos 60^circ - cos 80^circ])/(2 sin 10^circ)` = ______.
The value of `cos((41π)/4)` is ______.
The value of `2 cot^2(π/6) + 4 tan^2(π/6) - 3 "cosec"(π/6)` is ______.
Find the value of `cos ((29 π)/3)`.
sin2 17.5° + sin2 72.5° is equal to ______.
If cos θ = `- sqrt(3)/2` and sin α = `-3/5`, where θ does not and α lies in the third quadrant, then `(2 tan α + sqrt(3) tan θ)/(cot^2 θ + cos alpha)` is equal to ______.
If tan θ = `1/sqrt(7)`, then `(("cosec"^2θ - sec^2θ))/(("cosec"^2θ + sec^2θ))` is equal to ______.
If ΔABC is a right angled at C, then tan A + tan B 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 sin 930° is ______.
The value of sin 135° cosec 225° tan 150° cot 315° is ______.
The value of `(cos(90^circ + θ) sec(-θ)tan(180^circ - θ))/(sec(360^circ - θ)sin(180^circ + θ)cot(90^circ - θ))` is ______.
The value of tan 315° cot(– 405°) + cot 495° tan (– 585°).
The value of sin 150° cos 120° + cos 330° sin 660° is ______.
The value of `2 sin^2 π/6 + "cosec"^2 (7π)/6 cos^2 π/3` is ______.
cos2 5° + cos2 10° + cos2 15° + .... + cos2 85° + cos2 90° is equal to ______.
sin (270° – θ) sin (90° – θ) – cos ( 270° – θ) cos (90° + θ) is ______.
If x ≠ 0, then `(sin(pi + x)cos(pi/2 + x)tan((3pi)/2 - x)cot(2pi - x))/(sin(2pi - x)cos(2pi + x)cosec(-x)sin((3pi)/2 + x))` =
