Question
If $\sin(A +B) = 1(A -B) = 1,$ find $A$ and $B.$
✓
Answer
$\sin(A +B) = 1$
$\Rightarrow \sin(A + B) = \sin90^\circ $
$\Rightarrow A + B = 90^\circ .....(i)$
$\cos(A - B) = 1$
$\Rightarrow \cos(A - B) = \cos0^\circ $
$\Rightarrow A - B = 0^\circ ........(ii)$
Adding $(i)$ and $(ii)$
$A + B +A - B= 90^\circ + 0$
$2A = 90^\circ $
$A = 45^\circ $
Substituitng value of $A$ in $(i)$
$A + B = 90^\circ $
$45^\circ + B = 90^\circ$
$B = 45^\circ $
Therefore,
$A = B = 45^\circ .$
$\Rightarrow \sin(A + B) = \sin90^\circ $
$\Rightarrow A + B = 90^\circ .....(i)$
$\cos(A - B) = 1$
$\Rightarrow \cos(A - B) = \cos0^\circ $
$\Rightarrow A - B = 0^\circ ........(ii)$
Adding $(i)$ and $(ii)$
$A + B +A - B= 90^\circ + 0$
$2A = 90^\circ $
$A = 45^\circ $
Substituitng value of $A$ in $(i)$
$A + B = 90^\circ $
$45^\circ + B = 90^\circ$
$B = 45^\circ $
Therefore,
$A = B = 45^\circ .$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Solve, using cross$-$multiplication $:\sqrt2x - \sqrt3y = 0,\sqrt5x + \sqrt2y = 0$
→In the adjoining figure, $AB = AC$. If $DB \perp BC$ and EC $\perp BC$, prove that :
(i) $BD = CE$
(ii) $AD = AE$.
→(i) $BD = CE$
(ii) $AD = AE$.
Simplify the following:$2 \log 7+3 \log 5-\log \frac{49}{8}$
→The present age of a man is double the age of his son. After $8$ years, the ratio of their ages will be $7 : 4.$ Find the present ages of the man and his son.
→Simplify:
$\left(x+\frac{1}{x}\right)^2+\left(x-\frac{1}{x}\right)^2$
→$\left(x+\frac{1}{x}\right)^2+\left(x-\frac{1}{x}\right)^2$
Evaluate the following:$\frac{2^6 \times 5^{-4} \times 3^{-3} \times 4^2}{8^3 \times 15^{-3} \times 25^{-1}}$
→Draw a frequency polygon to represent the following data :
[Hint. Along x-axis, take 1 сm = ₹ 100. Along y-axis, take 2 cm = 10 workers.]
| Weekly wages (in) | 750 - 850 | 850 - 950 | 950 - 1050 | 1050 - 1150 | 1150 - 1250 |
| No. of workers | 52 | 41 | 65 | 54 | 38 |
Find the amount and the compound interest on the following :$Rs.15000$ for $2$ years at $8\%$ per annum compounded semi$-$annually.
→Trapezium given below; find its area.
The length of a rectangular field is thrice of its width. If the perimeter of this field is $1.6\ km$, find its area in $sq.m.$
→