Class 11MathematicsTrigonometrical Ratios, Functions and IdentitiesFundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles
EasyProve that $3 \sin \frac{\pi}{6} \sec \frac{\pi}{3} - 4 \sin \frac{5 \pi}{6} \cot \frac{\pi}{4} = 1$.
(N/A) We have the $L.H.S. = 3 \sin \frac{\pi}{6} \sec \frac{\pi}{3} - 4 \sin \frac{5 \pi}{6} \cot \frac{\pi}{4}$.
Using the values $\sin \frac{\pi}{6} = \frac{1}{2}$,$\sec \frac{\pi}{3} = 2$,$\sin \frac{5 \pi}{6} = \sin(\pi - \frac{\pi}{6}) = \sin \frac{\pi}{6} = \frac{1}{2}$,and $\cot \frac{\pi}{4} = 1$:
$L.H.S. = 3 \times \frac{1}{2} \times 2 - 4 \times \frac{1}{2} \times 1$
$L.H.S. = 3 - 2 = 1$
Since $L.H.S. = R.H.S. = 1$,the identity is proved.
Using the values $\sin \frac{\pi}{6} = \frac{1}{2}$,$\sec \frac{\pi}{3} = 2$,$\sin \frac{5 \pi}{6} = \sin(\pi - \frac{\pi}{6}) = \sin \frac{\pi}{6} = \frac{1}{2}$,and $\cot \frac{\pi}{4} = 1$:
$L.H.S. = 3 \times \frac{1}{2} \times 2 - 4 \times \frac{1}{2} \times 1$
$L.H.S. = 3 - 2 = 1$
Since $L.H.S. = R.H.S. = 1$,the identity is proved.
Explore More
Similar Questions
The value of $\frac{1+\tanh x}{1-\tanh x}$ is
If $\cosh x = \frac{\sqrt{14}}{3}$,$\sinh x = \cos \theta$ and $-\pi < \theta < -\frac{\pi}{2}$,then $\sin \theta =$
If $x = \tan 15^{\circ}$,$y = \operatorname{cosec} 75^{\circ}$ and $z = 4 \sin 18^{\circ}$,then :
DifficultAP EAMCET 2006
View SolutionThe value of $\cos 255^o + \sin 195^o$ is
DifficultAIEEE 2012
View SolutionIf $\sin(270^{\circ}-x^{\circ})=\cos 292^{\circ}$,then a value of $x$ is
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo