Question
Very-short and Short-Answer Questions.
Write the value of $\Big(\cot^2\theta+\frac{1}{\sin^2\theta}\Big).$
Write the value of $\Big(\cot^2\theta+\frac{1}{\sin^2\theta}\Big).$
✓
Answer
$\cot^2\theta+\frac{1}{\sin^2\theta}$$=\frac{\cos^2\theta}{\sin^2\theta}-\frac{1}{\sin^2\theta}$
$=\frac{\cos^2\theta-1}{\sin^2\theta}$
$=\frac{-\sin^2\theta}{\sin^2\theta}$ $\big(\sin^2\theta+\cos^2\theta=1\big)$
$=-1$
$=\frac{\cos^2\theta-1}{\sin^2\theta}$
$=\frac{-\sin^2\theta}{\sin^2\theta}$ $\big(\sin^2\theta+\cos^2\theta=1\big)$
$=-1$
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
The denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6. Find the fraction.
Calculate the height of an equilateral triangle each of whose sides measures $12cm$.
→A tree was broken due to storm. Its broken upper part was so inclined that its top touched the ground making an angle of 30°with the ground.The distance from the foot of the tree and the point where the top touched the ground was 10 metre. What was the height of the tree.
Prove the following.
secθ(1 - sinθ) (secθ + tanθ) = 1
secθ(1 - sinθ) (secθ + tanθ) = 1
Find:
The $15^{th}$ term of the AP $-40, -15, 10, 35, ....$
→The $15^{th}$ term of the AP $-40, -15, 10, 35, ....$
Find the coordinates of point P if P divides the line segment joining the points A(-1,7) and B(4,-3) in the ratio 2:3.
Find the diagonal of a rectangle whose length is $16\ cm$ and area is $192\ sq.cm.$
→The sum of the $2^{nd}$ and the $7^{th}$ terms of an AP is $30$. If its $15^{th}$ term is $1$ less than twice its $8^{th}$ term, find the AP.
→In the given figure, PA, QB and RC are each perpendicular to AC, Prove that $\frac{1}{\text{x}}+\frac{1}{\text{z}}=\frac{1}{\text{y}}.$
→If $\tan\theta=\frac{1}{\sqrt{2}},$ find the value of $\frac{\text{cosec}^2\theta-\sec^2\theta}{\text{cosec}^2\theta+\cot^2\theta}.$
→