Question
Prove the following identites:
$\big(\sec^2\theta-1\big)\cot^2\theta=1$
$\big(\sec^2\theta-1\big)\cot^2\theta=1$
✓
Answer
$\text{L.H.S.}=\big(\sec^2\theta-1\big)\cot^2\theta$
$=\tan^2\theta\times\cot^2\theta$ $\Big[\because\big(\sec^2\theta-1\big)=\tan^2\theta\Big]$
$=\tan^2\theta\times\frac{1}{\tan^2\theta}$
$=1$
$=\text{R.H.S.}$
$\therefore\text{LHS}=\text{RHS}$
$=\tan^2\theta\times\cot^2\theta$ $\Big[\because\big(\sec^2\theta-1\big)=\tan^2\theta\Big]$
$=\tan^2\theta\times\frac{1}{\tan^2\theta}$
$=1$
$=\text{R.H.S.}$
$\therefore\text{LHS}=\text{RHS}$
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 the $12^{\text {th }}$ term from the end of the following arithmetic progressions:
$3,5,7,9, \ldots . . ., 201$
→$3,5,7,9, \ldots . . ., 201$
Prove that, if two lines containing chords of a circle intersect each other outside the circle, then the measure of angle between them is half the difference in measures of the arcs intercepted by the angle.
In the figure given below DE || BC. If AD = 2.4cm, DB = 3.6cm, AC = 5cm. Find AE.
If the mean of 25 observations is 27 and each observation is decreased by 7, what will be the new mean?
If O is the center of the circle in the figure alongside, then complete the table from the given information.
The type of arc
The type of arc
| Type of circular arc | Name of circular arc | Measure of circular arc |
| Minor arc | ||
| Major arc |
Define HCF of two positive integers and find the HCF of the following pairs of numbers:
18 and 24
18 and 24
In a circle of radius 21cm, an arc subtends an angle of 60° at the centre Find the length of the arc.
Write the $n^{th}$^ ter, of the A.P. $\frac{1}{\text{m}},\frac{1+\text{m}}{\text{m}},\frac{1+2\text{m}}{\text{m}}, .....$
→Which value(s) of $\lambda,$ do the pair of linear equations $\lambda\text{x}+\text{y}=\lambda^2$ and $\text{x}+\lambda\text{y}=1$have:
Infinitely many solutions?
→Infinitely many solutions?
Solve the following quadratic equation by completing square method:
$m^2-2 m-1=0$
→$m^2-2 m-1=0$