Advertisements
Advertisements
प्रश्न
If A, B, C are the interior angles of a triangle ABC, prove that
`tan ((C+A)/2) = cot B/2`
उत्तर
We have to prove: `tan((C + A)/2) = cot B/2`
Since we know that in triangle ABC
A + B + C = 180
`=> C + A = 180^@ - B`
`=> (C + A)/2 = 90^@ - B/2`
`=> tan (C + A)/2 = tan (90^@ - B/2)`
`=> tan (C + A)/2 = cot B/2`
Proved
APPEARS IN
संबंधित प्रश्न
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
tan 65° + cot 49°
find the value of: sin 30° cos 30°
Evaluate:
`(cos3"A" – 2cos4"A")/(sin3"A" + 2sin4"A")` , when A = 15°
Prove that:
4 (sin4 30° + cos4 60°) -3 (cos2 45° - sin2 90°) = 2
If A =30o, then prove that :
sin 3A = 3 sin A - 4 sin3A.
If A = 30°;
show that:
4 cos A cos (60° - A). cos (60° + A) = cos 3A
Without using table, find the value of the following:
`(sin30° - sin90° + 2cos0°)/(tan30° tan60°)`
Without using tables, find the value of the following: `(tan45°)/("cosec"30°) + (sec60°)/(cot45°) - (5sin90°)/(2cos0°)`
Find the value of x in the following: `2sin x/(2)` = 1
In ΔABC right angled at B, ∠A = ∠C. Find the value of:
(i) sinA cosC + cosA sinC
(ii) sinA sinB + cosA cosB
