સાબિત કરો કે $\tan ^{4} \theta+\tan ^{2} \theta=\sec ^{4} \theta-\sec ^{2} \theta$
(N/A) ડા.બા. ($L$.$H$.$S$.) $= \tan ^{4} \theta + \tan ^{2} \theta$
$= \tan ^{2} \theta (\tan ^{2} \theta + 1)$
$= \tan ^{2} \theta \cdot \sec ^{2} \theta$ (કારણ કે $\sec ^{2} \theta = \tan ^{2} \theta + 1$)
$= (\sec ^{2} \theta - 1) \cdot \sec ^{2} \theta$ (કારણ કે $\tan ^{2} \theta = \sec ^{2} \theta - 1$)
$= \sec ^{4} \theta - \sec ^{2} \theta = \text{જ.બા. (R.H.S.)}$
$= \tan ^{2} \theta (\tan ^{2} \theta + 1)$
$= \tan ^{2} \theta \cdot \sec ^{2} \theta$ (કારણ કે $\sec ^{2} \theta = \tan ^{2} \theta + 1$)
$= (\sec ^{2} \theta - 1) \cdot \sec ^{2} \theta$ (કારણ કે $\tan ^{2} \theta = \sec ^{2} \theta - 1$)
$= \sec ^{4} \theta - \sec ^{2} \theta = \text{જ.બા. (R.H.S.)}$
Explore More
Similar Questions
જો $\sec 4A = \operatorname{cosec}(A - 20^{\circ})$ હોય,જ્યાં $4A$ એ લઘુકોણ છે,તો $A$ નું મૂલ્ય શોધો ($\circ$ માં).
Easy
View Solutionજો $\tan ^{2} \theta = \sin ^{2} \theta + \cos ^{2} \theta$ અને $0 < \theta < 90^{\circ}$ હોય,તો $\theta$ ની કિંમત ...... છે. ($^{\circ}$ માં)
Easy
View Solution$(1-\cos \theta)(1+\cos \theta) = \dots$
Easy
View Solution$\cos \theta = \frac{b}{\sqrt{a^2 + b^2}}$; જ્યાં,$0 < \theta < 90^\circ$; તો $\sin \theta = \dots$
Easy
View Solution$2 \sin ^{2} \theta+4 \sec ^{2} \theta+5 \cot ^{2} \theta+2 \cos ^{2} \theta-4 \tan ^{2} \theta-5 \operatorname{cosec}^{2} \theta = \dots$
Medium
View SolutionVedclass 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