Question
Prove : $\operatorname{cosec}^2 A-\cos ^2 A=\frac{\sec ^2 A-\sin ^2 A}{\tan ^2 A}$
✓
Answer
Get the step-by-step solution for this question inside the Vidyadip app.
Get the answer in the appNeed 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
Evaluate the following:
If A = 60° and B = 30°, verify that:
$\sin(\text{A}+\text{B})=\sin\text{A}\cos\text{B}+\cos\text{A}\sin\text{B}$
→If A = 60° and B = 30°, verify that:
$\sin(\text{A}+\text{B})=\sin\text{A}\cos\text{B}+\cos\text{A}\sin\text{B}$
>Radius of a sector of a circle is 7 cm. If measure of arc of the sector is –
(I) $30^{\circ}$
(II) $210^{\circ}$
(lll) three right angles
Find the area of sector in each case.
→(I) $30^{\circ}$
(II) $210^{\circ}$
(lll) three right angles
Find the area of sector in each case.
$3 m^2+2 m-7=0$
→In figure 3.88, circles with centres X and Y touch internally at point Z. Seg BZ is a chord of bigger circle and intersects smaller circle at point A. Prove that, seg AX || seg BY.
Find the HCF of $1008$ and $1080$ by prime factorization method.
→Find the indicated terms in the following sequences whose $n^{th}$ terms are:
$\text{a}_\text{n}=\frac{3\text{n}-2}{4\text{n}+5};\text{a}_7\text{ and }\text{a}_8$
→$\text{a}_\text{n}=\frac{3\text{n}-2}{4\text{n}+5};\text{a}_7\text{ and }\text{a}_8$
$\square ABCD$ is a trapezium in which $AB \| DC$ and its diagonals intersect each other at point $O$. Show that $A O: B O=C O: D O$.
→A tent of height $8.25m$ is in the form of a right circular cylinder with diameter of base $30m$ and height $5.5m$, surmounted by a right circular cone of the same base. Find the cost of the canvas of the tent at the rate of $₹\ 45\ per\ m^2.$
→Kalpana saves some amount every month. In first three months she saves $Rs.100,$
$Rs.150$ and $Rs.200$ respectively. In how many months will she save $Rs.1200?$
Activity :- Kalpana’s monthly saving is $Rs.100,Rs.150,Rs.200........Rs.1200$
Here $d=50.$Therefore this sequence is an A.P.
$a=10, d=50,$ $t _{ n }$___$ n=?$
$t _{ n }= a+(n-1)$____
_____$= 100+(n-1)\times 50$
$\frac{\square}{50}=n-1$
$n=\square$
therefore, she saves $Rs.1200$ in ____ months.
→$Rs.150$ and $Rs.200$ respectively. In how many months will she save $Rs.1200?$
Activity :- Kalpana’s monthly saving is $Rs.100,Rs.150,Rs.200........Rs.1200$
Here $d=50.$Therefore this sequence is an A.P.
$a=10, d=50,$ $t _{ n }$___$ n=?$
$t _{ n }= a+(n-1)$____
_____$= 100+(n-1)\times 50$
$\frac{\square}{50}=n-1$
$n=\square$
therefore, she saves $Rs.1200$ in ____ months.
The largest sphere is to be curved out of a right circular cylinder of radius $7\ cm$ and height $14\ cm$. Find the volume of the sphere.
→