Question
Write the value of $\cot^2\theta-\frac{1}{\sin^2\theta}$.
✓
Answer
We have,
$\cot^2\theta-\frac{1}{\sin^2\theta}=\cot^2\theta-\Big(\frac{1}{\sin\theta}\Big)^2$
$=\cot^2\theta-(\text{cosec }\theta)^2$
$=\cot^2\theta-\text{cosec}^2\theta$
We know that, $\cot^2\theta-\text{cosec}^2\theta=-1$
$\therefore\ \cot^2\theta-\frac{1}{\sin^2\theta}=-1$
$\cot^2\theta-\frac{1}{\sin^2\theta}=\cot^2\theta-\Big(\frac{1}{\sin\theta}\Big)^2$
$=\cot^2\theta-(\text{cosec }\theta)^2$
$=\cot^2\theta-\text{cosec}^2\theta$
We know that, $\cot^2\theta-\text{cosec}^2\theta=-1$
$\therefore\ \cot^2\theta-\frac{1}{\sin^2\theta}=-1$
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
Solve quadratic equation using formula : x² - 2x - 3 = 0
What is the distance between the points A(c, 0) and B(0, -c)?
In the given figure, PA and PB are tangents to the circle with centre O such that $\angle\text{APB}=50^{\circ}$. Write the measure of $\angle\text{OAB}.$
→Decide whether x = 2 and y =−1 is the solution of the equation 2x + y = 3 or not?
Find the area of the triangle with vertices $(a, b + c), (b, c + a)$ and $(c, a + b)$.
→Find the value of discriminant for each of the following equation.
$2 y^2-y+2=0$
→$2 y^2-y+2=0$
Find the probability that a number selected from the number 1 to 25 is not a prime number when each of the given numbers is equally likely to be selected.
$\triangle D E F \sim \triangle M N K$, If $D E=5$ and $M N=6$, then find the value of $A (\triangle DEF ): A (\triangle MNK )$
→The graph of the polynomial $f(x)=a x^2+b x+c$ is as shown below Fig. Write the signs of ' $a$ ' and $b^2-4 a c$, write the sign of $c$.
→In a circle of radius 6cm, a chord of length 10cm makes an angle of 110° at the centre of the circle. Find:
The circumference of the circle.
The circumference of the circle.