KCET · Maths · Trigonometric Ratios & Identities
\(\log \left(\sin 1^{\circ}\right) \cdot \log \left(\sin 2^{\circ}\right) \cdot \log \left(\sin 3^{\circ}\right)\) \(\ldots \log \left(\sin 179^{\circ}\right)\)
- A is positive
- B is negative
- C lies between 1 and 180
- D is zero
Answer & Solution
Correct Answer
(D) is zero
Step-by-step Solution
Detailed explanation
\(\log \left(\sin 1^{\circ}\right) \cdot \log \left(\sin 2^{\circ}\right) \cdot \log \left(\sin 3^{\circ}\right) \ldots \log \left(\sin 179^{\circ}\right)\)
\(=\log \sin 1^{\circ} \cdot \log \sin 2^{\circ} \ldots \log \sin 90^{\circ} \ldots \log \sin 179^{\circ}\)
\(=\log \sin 1^{\circ} \cdot \log \sin 2^{\circ} \ldots \log (1) \ldots \log \sin 179^{\circ}\)
\(\left.=\log \sin 1^{\circ} \cdot \log \sin 2 \ldots 0 \ldots \sin 90^{\circ}=1\right)\)
\(=0 \quad\left(\because \log \sin 179^{\circ} 1=0\right)\)
\(=\log \sin 1^{\circ} \cdot \log \sin 2^{\circ} \ldots \log \sin 90^{\circ} \ldots \log \sin 179^{\circ}\)
\(=\log \sin 1^{\circ} \cdot \log \sin 2^{\circ} \ldots \log (1) \ldots \log \sin 179^{\circ}\)
\(\left.=\log \sin 1^{\circ} \cdot \log \sin 2 \ldots 0 \ldots \sin 90^{\circ}=1\right)\)
\(=0 \quad\left(\because \log \sin 179^{\circ} 1=0\right)\)
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
- Foot of perpendicular drawn from the origin to the plane \( 2 x-3 y+4 z=29 \) isKCET 2015 Easy
- The point \((5,-7)\) lies outside the circleKCET 2008 Easy
- For constant \(a, \frac{d}{d x}\left(x^{x}+x^{a}+a^{x}+a^{a}\right)\) isKCET 2021 Medium
- The function \(f(x)=\sqrt{3} \sin 2 x-\cos 2 x+4\) is one-one in the intervalKCET 2021 Easy
- On the set of all natural numbers \(N\), which one of the following * is a binary operation?KCET 2009 Easy
- The shaded region shown in fig. is given by the inequation
KCET 2015 Hard
More PYQs from KCET
- If \( \cos y=x \cos (a+y) \) with \( \cos a \neq \pm 1 \), then \( \frac{d y}{d x} \) is equal toKCET 2018 Medium
- A uniform electric field in the plane of the paper as shown. Here \(A, B, C\) and \(D\) are the ponits on the circle. \(V_{1}, V_{2}, V_{3}\) and \(V_{4}\) are the potentials at those points respectively. Then
KCET 2013 Easy - Select the correct statement :KCET 2024 Easy
- The sum of the reciprocals of focal distances of a focal chord \(P Q\) of \(y^{2}=4 a x\) isKCET 2011 Easy
- The average power dissipated in A.C. circuit is \( 2 \) watt. If a current flowing through a circuit is \( 2 \)
\( A \) and impedance is \( 1 \Omega \), what is the power factor of the \( A C \) circuit?KCET 2014 Easy - The co-ordination number and the oxidation state of the element ' \( M \) ' in the complex
\( \left[\mathrm{M}(\mathrm{en})_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right] \mathrm{NO}_{2} \) [where (en) is ethan-1,2 - diamine] are respectivelyKCET 2017 Easy