Advertisements
Advertisements
Question
If A, B and C are the angles of a ΔABC, prove that tan `((C + "A")/2) = cot B/2`
Solution
In ΔABC
A + B + c = 180°
⇒ A + C = 180° - B ..........(i)
Now,
LHS `= tan (("C"+"A")/2)`
`=tan ((180^circ - "B")/2)` [Using (i)]
`= tan (90^circ - "B"/2)`
`= cot "B"/2 `
= RHS
APPEARS IN
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`((1+tan^2A)/(1+cot^2A))=((1-tanA)/(1-cotA))^2=tan^2A`
Without using trigonometric tables, evaluate :
`cot 38^circ/tan 52^circ`
Without using trigonometric tables, prove that:
cos 81° − sin 9° = 0
Without using trigonometric tables, prove that:
tan 71° − cot 19° = 0
Without using trigonometric tables, prove that:
tan48° tan23° tan42° tan67° = 1
Prove that:
`cos 80^circ/(sin 10^circ) + cos 59^circ "cosec" 31^circ = 2`
Prove that:
\[\frac{sin\theta \cos(90° - \theta)cos\theta}{\sin(90° - \theta)} + \frac{cos\theta \sin(90° - \theta)sin\theta}{\cos(90° - \theta)}\]
Prove that:
cos1° cos2° cos3° ... cos180° = 0
If sin 3 A = cos (A − 26°), where 3 A is an acute angle, find the value of A.
If tan 2 A = cot (A − 12°), where 2 A is an acute angle, find the value of A.
A man in a boat rowing away from a lighthouse 100 m high takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat in metres per minute [Use `sqrt3` = 1.732]
Without using trigonometric tables, find the value of (sin 72° + cos 18°)(sin 72° - cos 18°).
If 5 tan θ = 4, find the value of `(5 sin θ + 3 cos θ)/(5 sin θ + 2 cos θ)`
From the trigonometric table, write the values of cos 23°17'.
`(sin 40° + cos 50°)/(tan 38°20')`
Prove that:
`(sin^3 theta + cos^3 theta)/(sin theta + cos theta) = 1 - sin theta cos theta`
