Advertisements
Advertisements
प्रश्न
If `sin (A – B) = 1/2` and `cos (A + B) = 1/2`, `0^@` < A + `B <= 90^@`, A > B Find A and B.
उत्तर
`sin (A – B) = 1/2` and `cos (A + B) = 1/2`
Now `sin (A - B) = 1/2`
`=> sin (A- B) = sin 30^@`
`=> A - B( = 30^@` ....(1)
And `cos (A + B) = 1/2`
`=> cos (A + B) = cos 60^@`
`=> A + B = 60^@` ...(2)
Adding (1) and (2) we get
`2A = 90^@`
`=> A = 90^@/2 = 45^@`
Put `A = 45^@` in (2 ) we get
`=> 45^@ + B = 60^@`
`=> B = 60^@ - 45^@``
`=>B = 15^@`
Thus `A = 45^@ and B = 15^@`
संबंधित प्रश्न
If 8 tan A = 15, find sin A – cos A.
If A = 450, verify that :
(i) sin 2A = 2 sin A cos A
Given: sin θ = `p/q`.
Find cos θ + sin θ in terms of p and q.
If cot θ= 1; find the value of: 5 tan2 θ+ 2 sin2 θ- 3
From the following figure, find:
(i) y
(ii) sin x°
(iii) (sec x° - tan x°) (sec x° + tan x°)
In rhombus ABCD, diagonals AC and BD intersect each other at point O.
If cosine of angle CAB is 0.6 and OB = 8 cm, find the lengths of the side and the diagonals of the rhombus.
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
sinA = `(12)/(13)`
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
cose C = `(15)/(11)`
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
tanB = `(8)/(15)`
If A + B = 90°, cot B = `3/4` then tan A is equal to ______.
