AP EAMCET · Maths · Inverse Trigonometric Functions
If \(\sec ^{-1} \frac{x}{a}-\sec ^{-1} \frac{x}{b}=\sec ^{-1} b \sec ^{-1} a\), then \(x\) is equal to
- A \(a b\)
- B \(-a b\)
- C \(a^2\)
- D \(b^2\)
Answer & Solution
Correct Answer
(A) \(a b\)
Step-by-step Solution
Detailed explanation
\(\sec ^{-1}\left(\frac{x}{a}\right)-\sec ^{-1}\left(\frac{x}{b}\right)=\sec ^{-1} b-\sec ^{-1} a\) \(\cos ^{-1}\left(\frac{a}{x}\right)-\cos ^{-1}\left(\frac{b}{x}\right)=\cos ^{-1}\left(\frac{1}{b}\right)-\cos ^{-1}\left(\frac{1}{a}\right)\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\int \frac{d x}{7+5 \cos x}\) is equal toAP EAMCET 2002 Medium
- If \(\sec (\theta+\alpha), \sec \theta\) and \(\sec (\theta-\alpha)\) are arithmetic progression, then \(\sin ^2 \theta=\)AP EAMCET 2023 Easy
- Assertion (A)
\[
\int_2^e\left(\frac{1}{\log _e x}-\frac{1}{\left(\log _e x\right)^2}\right) d x=e-2 \log _2 e
\]
Reason (R)
\[
\int_a^b e^x\left(f(x)+f^{\prime}(x)\right) d x=e^b f(b)-e^a f(a)
\]AP EAMCET 2022 Medium - If the coefficients of \(x^5\) and \(x^6\) are equal in the expansion of \(\left(a+\frac{x}{5}\right)^{65}\), then the coefficient of \(x^2\) in the expansion of \(\left(a+\frac{x}{5}\right)^4\) isAP EAMCET 2024 Easy
- If \(\mathrm{y}=(\mathrm{ax}+\mathrm{b}) \cos \mathrm{x}\), then \(\mathrm{y}_2+\mathrm{y}_1 \sin 2 \mathrm{x}+\mathrm{y}\left(1+\sin ^2 \mathrm{x}\right)=\)AP EAMCET 2025 Medium
- \(A(a, 0)\) is a fixed point and \(\theta\) is a parameter such that \(0 < \theta < 2 \pi\). If \(\mathrm{P}(\mathrm{a} \cos \theta, \mathrm{a} \sin \theta)\) is a point on the circle \(\mathrm{x}^2+\mathrm{y}^2=\mathrm{a}^2\) and \(\mathrm{Q}(\mathrm{b} \sin \theta,-\mathrm{b} \cos \theta)\) is a point on the circle \(x^2+y^2=b^2\), then the locus of the centroid of the triangle APQ isAP EAMCET 2025 Medium
More PYQs from AP EAMCET
- If \(P=(2,-3,4), Q=(-1,-4,0), R=(2,1,0)\) are three points and \(S\) is the foot of the perpendicular drawn from \(\mathrm{R}\) to \(\mathrm{PQ}\), then the \(\mathrm{X}\)-coordinate of \(\mathrm{S}\) isAP EAMCET 2018 Medium
- \(\int_0^1 \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x=\)AP EAMCET 2020 Medium
- If the chord of the ellipse \(\frac{x^2}{4}+\frac{y^2}{9}=1\) having \((1,1)\) as its middle point is \(\dot{x}+\alpha y=\beta\), thenAP EAMCET 2024 Easy
- A battery of \(e m f 8 \mathrm{~V}\) and internal resistance \(0.5 \Omega\) is being charged by a 120 V dc supply using a series resistor of \(15.5 \Omega\). The terminal voltage of 8 V battery during charging isAP EAMCET 2024 Medium
- The product formed when formaldehyde reacts with ammonia isAP EAMCET 2020 Medium
- A \(6 \mathrm{~V}\) cell with \(0.5 \Omega\) internal resistance, a \(10 \mathrm{~V}\) cell with \(1 \Omega\) internal resistance and a \(12 \Omega\) external resistance are connected in parallel. The current (in ampere) through the \(10 \mathrm{~V}\) cell isAP EAMCET 2005 Medium