Advertisements
Advertisements
प्रश्न
In ΔABC, A + B + C = π show that
tan 2A + tan 2B + tan 2C = tan 2A tan 2B tan 2C
Advertisements
उत्तर
In ΔABC,
A + B + C = π
∴ 2A + 2B + 2C = 2π
∴ 2A + 2B = 2π – 2C
∴ tan (2A + 2B) = tan (2π – 2C)
∴ `(tan2"A" + tan2"B")/(1 - tan2"A"*tan2"B")` = – tan 2C
∴ tan 2A + tan 2B = − tan 2C . (1 − tan 2A . tan 2B)
∴ tan 2A + tan 2B = – tan 2C + tan 2A· tan 2B· tan 2C
∴ tan 2A + tan 2B + tan 2C = tan 2A · tan 2B· tan 2C
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
`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:
`(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
The area of the Δ ABC is `10sqrt3` cm2, angle B is 60° and its perimeter is 20 cm , then l(AC) = ______.
In a ΔABC, A : B : C = 3 : 5 : 4. Then `a + b + csqrt2` is equal to ______
If A, B, C are the angles of ΔABC then cotA.cotB + cotB. cotC + cotC + cotA = ______.
If A + B = C, then cos2 A + cos2 B + cos2 C – 2 cos A cos B cos C is equal to ______.
If A + B + C = 180°, then `sum tan A/2 tan B/2` is ______.
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 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 + B + C = π(A, B, C > 0) and the ∠C is obtuse, then ______.
If a ΔABC, the value of sin A + sin B + sin C is ______.
If A + B + C = 270°, then cos 2A + cos 2B + cos 2C + 4 sin A sin B sin C is equal to ______.
If A + B = C = 180°, then the value of `cot A/2 + cot B/2 + cot C/2` will be ______.
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 `tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2` is ______.
