Advertisements
Advertisements
Question
If tan (A + B) = `sqrt3` and tan (A – B) = `1/sqrt3`; 0° < A + B ≤ 90°; A > B, find A and B.
Solution 1
tan (A + B) = `sqrt(3)` = tan 60° and tan (A – B) = `1/sqrt(3)` = tan 30°
A + B = 60° ...(1)
A – B = 30° ...(2)
2A = 90°
⇒ A = 45°
Adding (1) and (2)
A + B = 60°
A – B = 30°
Subtract equation (2) from (1)
A + B = 60°
A – B = 30°
2B = 30°
⇒ B = 15°
Note: sin(A + B) = sin A cos B + cos A sin B
sin(A + B) ≠ sin A + sin B
Solution 2
Here, tan (A – B) = `1/sqrt(3)`
⇒ tan (A – B) = tan 30° ...[∵ tan 30° = `1/sqrt(3)`]
⇒ (A – B) = 30° ...(i)
Also, tan (A + B) = `sqrt(3)`
⇒ tan (A + B) = tan 60° ...[∵ tan 60° = `sqrt(3)`]
⇒ A + B = 60° ...(ii)
Solving (i) and (ii), we get:
A = 45° and B = 15°
APPEARS IN
RELATED QUESTIONS
Evaluate cos 48° − sin 42°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
sec 76° + cosec 52°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cosec 54° + sin 72°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
sin 67° + cos 75°
If A, B, C are the interior angles of a triangle ABC, prove that
`tan ((C+A)/2) = cot B/2`
Prove that `sin 70^@/cos 20^@ + (cosec 20^@)/sec 70^@ - 2 cos 20^@ cosec 20^@ = 0`
Prove that
tan (55° − θ) − cot (35° + θ) = 0
find the value of: sin 30° cos 30°
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios: sin 45°
If sin x = cos y, then x + y = 45° ; write true of false
find the value of :
3sin2 30° + 2tan2 60° - 5cos2 45°
Prove that:
cos2 30° - sin2 30° = cos 60°
secθ . Cot θ= cosecθ ; write true or false
If A = 30°;
show that:
cos 2A = cos4 A - sin4 A
If A = 30°;
show that:
`(1 + sin 2"A" + cos 2"A")/(sin "A" + cos"A") = 2 cos "A"`
If A = 30°;
show that:
`(cos^3"A" – cos 3"A")/(cos "A") + (sin^3"A" + sin3"A")/(sin"A") = 3`
Without using tables, evaluate the following: (sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°).
Find the value of x in the following: 2 sin3x = `sqrt(3)`
If sin(A + B) = 1 and cos(A – B)= `sqrt(3)/2`, 0° < A + B ≤ 90° and A > B, then find the measures of angles A and B.
If A and B are acute angles such that sin (A – B) = 0 and 2 cos (A + B) – 1 = 0, then find angles A and B.
