MCQ
$(\text{cosec }\theta-\sin\theta)(\sec\theta-\cos\theta)(\tan\theta+\cot\theta)$ is equal to :
- A$0$
- ✓$1$
- C$-1$
- DNone of these.
✓
Answer
Correct option: B.
$1$
$(\text{cosec }\theta-\sin\theta)(\sec\theta-\cos\theta)(\tan\theta+\cot\theta)$
$=\Big(\frac{1}{\sin\theta}-\sin\theta\Big)\Big(\frac{1}{\cos\theta}-\cos\theta\Big)$
$\Big(\frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta}\Big)$
$=\frac{1-\sin^2\theta}{\sin\theta}\times\frac{1-\cos^2\theta}{\cos\theta}\times\frac{\sin^2\theta+\cos^2\theta}{\sin\theta\cos\theta}$
$=\frac{\cos^2\theta}{\sin\theta}\times\frac{\sin^2\theta}{\cos\theta}\times\frac{1}{\sin\theta\cos\theta}$
$=\frac{\sin^2\theta\cos^2\theta}{\sin^2\theta\cos^2\theta}=1$
$=\Big(\frac{1}{\sin\theta}-\sin\theta\Big)\Big(\frac{1}{\cos\theta}-\cos\theta\Big)$
$\Big(\frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta}\Big)$
$=\frac{1-\sin^2\theta}{\sin\theta}\times\frac{1-\cos^2\theta}{\cos\theta}\times\frac{\sin^2\theta+\cos^2\theta}{\sin\theta\cos\theta}$
$=\frac{\cos^2\theta}{\sin\theta}\times\frac{\sin^2\theta}{\cos\theta}\times\frac{1}{\sin\theta\cos\theta}$
$=\frac{\sin^2\theta\cos^2\theta}{\sin^2\theta\cos^2\theta}=1$
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
The curved surface area of a cone having height 24 cm and radius 7 cm, is
The distance of the point $(3,5)$ from the $x$-axis is
→In the given figure if $B P\|C F, D P\| E F$, then $AD : DE$ is equal to
→$500$ bananas were divided equally among a certain number of students. If there were $25$ more students, each would have received one banana less. Then the number of students is :
→In a $\triangle A B C, A D$ is the bisector of $\angle B A C$. If $A B=6 cm, A C=5 cm$ and $B D=3 cm$, then $D C=$
→$\triangle D E F \sim \triangle A B C$; If $D E: A B=2: 3$ and $\operatorname{ar}(\triangle D E F)$ is equal to $44 $ square units, then area $(\triangle A B C)$ in square units is
→A solid consists of a circular cylinder surmounted by a right circular cone. The height of the cone is h. If the total height of the solid is 3 times the volume of the cone, then the height of the cylinder is:
If the sum of the roots of the equation $x^2-(k+6) x+2(2 k-1)=0$ is equal to half of the: product, then $k=$
→A bag contains 8 red, 2 black and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is not black?
In a $\triangle\text{ABC},$ it is given that $AD$ is the internal bisector of $\angle\text{A}.$ If $AB = 10\ cm, AC = 14\ cm$ and $BC = 6\ cm,$ then $CD = ?$
→