Question
Write the value of $\sin\text{A}\cos(90^\circ-\text{A})+\cos\text{A}\sin(90^\circ-\text{A})$.
✓
Answer
$\sin\text{A}\cos(90^\circ-\text{A})+\cos\text{A}\sin(90^\circ-\text{A})$
$=\sin\text{A}\sin\text{A}+\cos\text{A}\cos\text{A}$
$\begin{cases}\because \cos(90^\circ-\text{A})=\sin\text{A} \\ \sin(90^\circ-\text{A})=\cos\text{A} \\ \sin^2\text{A}+\cos^2\text{A}=1\end{cases}$
$=\sin^2\text{A}+\cos^2\text{A}=1$
$=\sin\text{A}\sin\text{A}+\cos\text{A}\cos\text{A}$
$\begin{cases}\because \cos(90^\circ-\text{A})=\sin\text{A} \\ \sin(90^\circ-\text{A})=\cos\text{A} \\ \sin^2\text{A}+\cos^2\text{A}=1\end{cases}$
$=\sin^2\text{A}+\cos^2\text{A}=1$
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
Find:Which term in the A.P. $21,42,63,84, \ldots .$. is 420 ?
→If (x, y) be on the line joining the two points (1, -3) and (-4, 2), prove that x + y + 2= 0.
Two APs have the same common difference. The difference between their 100th terms is $100$, what is the difference between their $1000th$ terms?
→Suppose we throw a die once.
- What is the probability of getting a number greater than 4?
- What is the probability of getting a number less than or equal to 4?
A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete.
Each step has a rise of $\frac{1}{4}$m and a tread of $\frac{1}{2}$m. (see figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = $\frac 14 \times \frac 12 \times$ 50 $m^3$]
→Each step has a rise of $\frac{1}{4}$m and a tread of $\frac{1}{2}$m. (see figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = $\frac 14 \times \frac 12 \times$ 50 $m^3$]
By what number should 1365 be divided to get 31 as quotient and 32 as remainder?
In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula $\bar{\text{x}}=\text{a}+\frac{\sum\text{f}_\text{i}\text{d}_\text{i}}{\sum\text{f}_\text{i}}$ where a is the assumed mean. a must be one of the mid-points of the classes. Is the last statement correct? Justify your answer.
→Prove that:
$\frac{\sec(90^\circ-\theta)\text{cosec }\theta-\tan(90^\circ-\theta)\cot\theta+\cos^225^\circ+\cos^265^\circ}{3\tan27^\circ\tan63^\circ}=\frac{2}{3}$
→$\frac{\sec(90^\circ-\theta)\text{cosec }\theta-\tan(90^\circ-\theta)\cot\theta+\cos^225^\circ+\cos^265^\circ}{3\tan27^\circ\tan63^\circ}=\frac{2}{3}$
What is a composite number?
In the given figure, $\angle ABC =\angle ACB$ and $\frac{B C}{B E}=\frac{B D}{A C}$.
Show that $\angle ABE \sim \angle DBC$ and $AE \| DC$.
→Show that $\angle ABE \sim \angle DBC$ and $AE \| DC$.