Question
What is the value of $\frac{\tan^2\theta-\sec^2\theta}{\cot^2\theta-\text{cosec}^2\theta}?$
✓
Answer
$\frac{\tan^2\theta-\sec^2\theta}{\cot^2\theta-\text{cosec}^2\theta}=\frac{-(\sec^2\theta-\tan^2\theta)}{-(\text{cosec}^2\theta-\cot^2\theta)}$
$=\frac{-1}{-1}=1 \ \begin{cases}\because \sec^2\theta-\tan^2\theta= 1 \\ \text{cosec}^2\theta-\cot^2\theta=1 \end{cases}$
$=\frac{-1}{-1}=1 \ \begin{cases}\because \sec^2\theta-\tan^2\theta= 1 \\ \text{cosec}^2\theta-\cot^2\theta=1 \end{cases}$
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 sum of the following APs:
2, 7, 12, 17, .... to 19 terms.
2, 7, 12, 17, .... to 19 terms.
Write the family of quadratic polynomials having $-\frac{1}{4}$ and 1 as its zeros.
→If $\text{cosec }\theta-\cot\theta=\alpha,$ write the value of $\text{cosec }\theta+\cos\alpha$.
→Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
□ ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T. Prove that DE × BE = CE × TE.
Find the $8^{th}$ term from the end of the A.P. $7, 10, 13,... 184.$
→If $a \neq b \neq 0$, prove that the points $\left(a, a^2\right),\left(b, b^2\right),(0,0)$ will not be collinear.
→Two concentric circle are of radii $6.5\ cm$ and $2.5\ cm$. Find the length of the chord of the larger circle which touches the smaller circle.
→Basketball players John, Vasim, Akash were practising the ball drop in the basket. The probabilities of success for John, Vasim and Akash are 4/5 0.83 and 58% respectively. Who had the greatest probability of success?
Find:Which term in the A.P. $21, 42, 63, 84$, ..... is $420$?
→