Advertisements
Advertisements
प्रश्न
Prove the following:
sin47° + sin61° − sin11° − sin25° = cos7°
Advertisements
उत्तर
L.H.S. = sin47° + sin61° − sin11° − sin25°
= (sin47° − sin25°) + (sin61° − sin11°)
= `2cos((47^circ + 25^circ)/2)*sin ((47^circ - 25^circ)/2) + 2cos((61^circ + 11^circ)/2)*sin((61^circ - 11^circ)/2)`
= 2cos36° · sin11° + 2cos36° · sin25°
= 2cos36° (sin25° + sin11°)
= `2cos36^circ xx 2sin((25^circ + 11^circ)/2)*cos((25^circ - 11^circ)/2)`
= 4cos36° · sin18° · cos7°
= `4 xx (sqrt(5) + 1)/4 xx (sqrt(5) - 1)/4 xx cos7^circ ...[because cos36^circ = (sqrt(5) + 1)/4, sin 18^circ = (sqrt(5) - 1)/4]`
= `(4(5 - 1))/16 cos7^circ`
= cos7°
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the values of:
tan 105°
Find the value of sin 690°.
Find the value of :
tan 225°
Find the value of :
tan (– 690°)
Find the value of:
sec (–855°)
Find the value of :
cosec 780°
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:
sin 18° = `(sqrt(5) - 1)/4`
Prove the following:
cos 36° = `(sqrt(5) + 1)/4`
Prove the following:
`tan pi/8 = sqrt(2) - 1`
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(– 1125°) is ______.
The value of `cos((41π)/4)` is ______.
The value of `cos π/8 + cos (3π)/8 + cos (5π)/8 + cos (7π)/8` 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)`.
The value of cos 480° sin 150° + sin 600° cos 390° is ______.
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 sin A + sin B + sin C = 3, then cos A + cos B + cos C 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 `(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 sin 150° cos 120° + cos 330° sin 660° 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 ______.
