Advertisements
Advertisements
प्रश्न
Prove the following:
`cos (2pi)/15 cos (4pi)/15cos (8pi)/15cos (16pi)/15 = 1/16`
Advertisements
उत्तर
L.H.S. = `cos (2pi)/15 cos (4pi)/15cos (8pi)/15cos (16pi)/15`
= `((2sin (2pi)/15*cos (2pi)/15)*cos (4pi)/15*cos (8pi)/15*cos (16pi)/15)/(2sin (2pi)/15)`
= `(sin (4pi)/15*cos (4pi)/15*cos (8pi)/15*cos (16pi)/15)/(2sin (2pi)/15)`
= `((2sin (4pi)/15*cos (4pi)/15)cos (8pi)/15*cos (16pi)/15)/(4sin (2pi)/15)`
= `(sin (8pi)/15*cos (8pi)/15*cos (16pi)/15)/(4sin (2pi)/15)`
= `((2sin (8pi)/15*cos (8pi)/15)cos (16pi)/15)/(8sin (2pi)/15)`
= `(sin (16pi)/15*cos (16pi)/15)/(8sin (2pi)/15)`
= `(2sin (16pi)/15*cos (16pi)/15)/(16sin (2pi)/15)`
= `(sin (32pi)/15)/(16sin (2pi)/15)`
= `(sin(2pi + (2pi)/15))/(16sin (2pi)/15)`
= `(sin (2pi)/15)/(16sin (2pi)/15)`
= `1/16`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
In ΔABC, A + B + C = π show that
cos 2A + cos 2B + cos 2C = –1 – 4 cos A cos B cos C
In ΔABC, A + B + C = π show that
cos A + cos B – cos C = `4cos "A"/2 cos "B"/2 sin "C"/2 - 1`
In ΔABC, A + B + C = π show that
sin2A + sin2B − sin2C = 2 sin A sin B cos C
In ΔABC, A + B + C = π show that
`sin^2 "A"/2 + sin^2 "B"/2 - sin^2 "C"/2 = 1 - 2cos "A"/2 cos "B"/2 sin "C"/2`
Prove the following:
If sin α sin β − cos α cos β + 1 = 0 then prove cot α tan β = −1
Prove the following:
`(1 + cos pi/8)(1 + cos (3pi)/8)(1 + cos (5pi)/8)(1 + cos (7pi)/8) = 1/8`
Prove the following:
If A + B + C = `(3pi)/2`, then cos 2A + cos 2B + cos 2C = 1 − 4 sin A sin B sin C
Prove the following:
In ∆ABC, ∠C = `(2pi)/3`, then prove that cos2A + cos2B − cos A cos B = `3/4`
The area of the Δ ABC is `10sqrt3` cm2, angle B is 60° and its perimeter is 20 cm , then l(AC) = ______.
If `cos "A" = 3/4,`then 32 sin`"A"/2 cos (5"A")/2` = ?
`(sin20^circ +2sin40^circ)/sin70^circ=` ______.
If A, B, C are the angles of ΔABC then cotA.cotB + cotB. cotC + cotC + cotA = ______.
If A + B + C = π, then sin 2A + sin 2B + sin 2C is equal to ______.
If A + B = C, then cos2 A + cos2 B + cos2 C – 2 cos A cos B cos C is equal to ______.
If α + β – γ = π, then sin2 α + sin2 β – sin2 γ is equal to ______.
If A + B + C = 180°, then `sum tan A/2 tan B/2` is ______.
Let A, B and C are the angles of a triangle and `tan(A/2) = 1/3, tan(B/2) = 2/3`. Then, `tan(C/2)` is equal to ______.
If A + B + C = π, then cos2 A + cos2 B + cos2 C is equal to ______.
ΔABC is a right angled isosceles triangle with ∠B = 90°. If D is a point on AB, ∠CDB = 15° and AD = 35 cm, then CD is equal to ______.
If sin A + sin B = C, cos A + cos B = D, then the value of sin(A + B) = ______.
If A + B + C = π and sin C + sin A cos B = 0, then tan A . cot B is equal to ______.
If x + y + z = 180°, then cos 2x + cos 2y – cos 2z is equal to ______.
If a ΔABC, the value of sin A + sin B + sin C is ______.
If A, B, C are the angles of a triangle, then sin2 A + sin2 B + sin2 C – 2 cos A cos B cos C is equal to ______.
In any ΔABC, if tan A + tan B + tan C = 6 and tan A tan B = 2, then the values of tan A, tan B and tan C are ______.
If cos A = cos B cos C and A + B + C = π, then the value of cot B cot C is ______.
