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Yogita Ingle 5 years, 2 months ago
Δ ABC is a Right Triangle at ∠C = 90°
To Find:
sin A × cos B + cos A × sin B = ?
Solution:
Δ ABC is a Right Triangle at ∠C = 90° .......Given
Also
Therefore,
∠ A = 30°
Now in ΔABC
.........angle sum Triangle property
substituting the values we get
So the value of
sin A × cos B + cos A × sin B =
Therefore
sin A × cos B + cos A × sin B = 1
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Yogita Ingle 5 years, 2 months ago
The number series 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, . . . . , 240.
The first term a = 8
The common difference d = 8
Total number of terms n = 30
step 2 apply the input parameter values in the AP formula
Sum = n/2 x (a + Tn)
= 30/2 x (8 + 240)
= (30 x 248)/ 2
= 7440/2
8 + 16 + 24 + 32 + 40 + 48 + 56 + 64 + 72 + 80 + 88 + 96 + . . . . + 240 = 3720
Therefore, 3720 is the sum of first 30 positive integers which are divisible by 8
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Yogita Ingle 5 years, 2 months ago
1032=408×2 + 216
408 = 216×1 + 192
216 = 192×1 + 24
192=24×8 + 0
so the hcf will be 24
now
24 = 1032 - 408×5
1032m - 2040 = 24
m=2
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Yogita Ingle 5 years, 2 months ago
(i) 140 = 2 x 2 x 5 x 7 =2² x 5 x 7
(ii)156 =2 x 2 x 3 x 13 =2² x 3 x 13
(iii)3825 =3 x 3 x 5 x 5 x 17 =3² x 5² x 17
(iv)5005 =5 x 7 x 11 x 13 =5 x 7 x 11 x 13
(v)7429 =17 x 19 x 23 =17 x 19 x 23
2Thank You