Advertisements
Advertisements
प्रश्न
Prove the following:
If sin α sin β − cos α cos β + 1 = 0 then prove cot α tan β = −1
Advertisements
उत्तर
sin α sin β − cos α cos β + 1 = 0
∴ cos α cos β − sin α sin β = 1
∴ cos (α + β) = 1
∴ α + β = 0 ...[∵ cos 0 = 1]
∴ β = − α
L.H.S. = cot α tan β
= cot α tan (− α)
= − cot α tan α
= − 1
= 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
sin A + sin B + sin C = `4cos "A"/2 cos "B"/2 cos "C"/2 `
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
`tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2tan "A"/2` = 1
In ΔABC, A + B + C = π show that
`cot "A"/2 + cot "B"/2 + cot "C"/2 = cot "A"/2 cot "B"/2 cot "C"/2`
Prove the following:
`cos (2pi)/15 cos (4pi)/15cos (8pi)/15cos (16pi)/15 = 1/16`
Prove the following:
`(1 + cos pi/8)(1 + cos (3pi)/8)(1 + cos (5pi)/8)(1 + cos (7pi)/8) = 1/8`
Prove the following:
In ∆ABC, ∠C = `(2pi)/3`, then prove that cos2A + cos2B − cos A cos B = `3/4`
In a ΔABC, A : B : C = 3 : 5 : 4. Then `a + b + csqrt2` is equal to ______
The value of `[(1 - cos pi/6 + isin pi/6)/(1 - cos pi/6 - isin pi/6)]^6` = ______
If `cos "A" = 3/4,`then 32 sin`"A"/2 cos (5"A")/2` = ?
`(sin20^circ +2sin40^circ)/sin70^circ=` ______.
If A + B + C = π, then sin 2A + sin 2B + sin 2C is equal to ______.
In a ΔABC, `cos((B + 2C + 3A)/2) + cos((A - B)/2)` is ______.
If A + B + C = 270°, then cos 2A + cos 2B + cos 2C is equal to ______.
If A + B + C = π, then sin 2A + sin 2B – sin 2C is equal to ______.
In a ΔABC, if cos A cos B cos C = `(sqrt(3) - 1)/8` and sin A sin B sin C = `(3 + sqrt(3))/8`, then the angles of the triangle are ______.
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 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 = 180°, then the value of `cot A/2 + cot B/2 + cot C/2` will be ______.
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 A + B + C = 180°, then `(sin 2A + sin 2B + sin 2C)/(cos A + cos B + cos C - 1)` is equal to ______.
If cos A = cos B cos C and A + B + C = π, then the value of cot B cot C is ______.
The value of cot A cot B + cot B cot C + cot C cot A is ______.
The value of `tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2` is ______.
