AP EAMCET · Maths · Inverse Trigonometric Functions
\(\operatorname{sech}^{-1}(\sin \theta)\) is equal to
- A \(\log \tan \frac{\theta}{2}\)
- B \(\log \sin \frac{\theta}{2}\)
- C \(\log \cos \frac{\theta}{2}\)
- D \(\log \cot \frac{\theta}{2}\)
Answer & Solution
Correct Answer
(D) \(\log \cot \frac{\theta}{2}\)
Step-by-step Solution
Detailed explanation
We have, sech \({ }^{-1}(\sin \theta)\) \(\begin{aligned} & =\cos h^{-1}(\operatorname{cosec} \theta) \\ & =\log \left[\operatorname{cosec} \theta+\sqrt{\left(\operatorname{cosec}^2 \theta-1\right)}\right] \\ & =\log \cot \frac{\theta}{2}\end{aligned}\)
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
- Area of the triangle formed by the lines \(3 x^2-4 x y+y^2=0,2 x-y=6\) isAP EAMCET 2004 Medium
- If the chord of contact of the point \(\mathrm{P}(\mathrm{h}, \mathrm{k})\) with respect to the circle \(x^2+y^2-4 x-4 y+8=0\) meets the circle in two distinct points and it also makes an angle \(45^{\circ}\) with the positive \(\mathrm{X}\)-axis in the positive direction, then \((\mathrm{h}, \mathrm{k})\) cannot beAP EAMCET 2023 Easy
- The set \(\left\{x \in \mathbb{R}: 16\left(2^X\right)>16^{\frac{-1}{x}}\right\}=\)AP EAMCET 2023 Easy
- Consider two systems of 3 linear equations in 3 unknowns \(\mathrm{AX}=\mathrm{B}\) and \(C X=D\). If \(A X=B\) has unique solution \(D\) and \(C X=D\) has unique solution \(B\), then the solution of \(\left(\mathrm{A}-\mathrm{C}^{-1}\right) \mathrm{X}=\mathrm{O}\) isAP EAMCET 2025 Medium
- \(f(x)\) and \(g(x)\) are differentiable functions such that \(\frac{f(x)}{g(x)}=\) a non zero constant. If \(\frac{\mathrm{f}^{\prime}(\mathrm{x})}{\mathrm{g}^{\prime}(\mathrm{x})}=\alpha(\mathrm{x})\) and \(\left(\frac{\mathrm{f}(\mathrm{x})}{\mathrm{g}(\mathrm{x})}\right)^{\prime}=\beta(\mathrm{x})\), then \(\frac{\alpha(x)-\beta(x)}{\alpha(x)+\beta(x)}=\)AP EAMCET 2023 Hard
- A line has slope and -intercept 4. The distance between the origin and the line is equal toAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- \(\lim _{x \rightarrow 0}\left(\frac{\sin a x}{\tan b x}\right)\) is equal toAP EAMCET 2021 Easy
- The concentration of IL of \(\mathrm{CaCO}_3\) solution is 1000 ppm . What is its concentration in \(\mathrm{mol} \mathrm{L}^{-1}\) ?
\((\mathrm{Ca}=40 \mathrm{u}, \mathrm{O}=16 \mathrm{u}, \mathrm{C}=12 \mathrm{u})\)AP EAMCET 2024 Medium - The number of valence electrons present in an element with atomic number 117 isAP EAMCET 2022 Easy
- The product formed when formaldehyde reacts with ammonia isAP EAMCET 2020 Medium
- In a communication system operating at wavelength \(800 \mathrm{~nm}\), only one per cent of source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of bandwidth \(6 \mathrm{MHz}\) isAP EAMCET 2021 Medium
- An angle between the curves \(x^2 y=1\) and \(y\left(x^2+1\right)=2\) isAP EAMCET 2017 Medium