Question

If sec theta + tan theta = m , then the value of sec^4theta - tan^4theta - 2 sec theta tan theta is-----------.​

Answer 1

Step-by-step explanation:

$\sf \blue{sec \theta + tan \theta = m} \\ \sf \red{sec {}^{4} \theta - tan {}^{4} \theta - 2sec \theta.tan \theta =?} \\ \sf \green{(sec {}^{2} \theta - tan {}^{2} \theta) {}^{2} - 2sec \theta.tan \theta} \\ \sf \green{(1) {}^{2} - 2 \frac{1}{cos \theta} \times \frac{sin \theta}{cos \theta} } \\ \sf \green{1 - \frac{2sin \theta}{cos {}^{2} \theta} } \\ \sf \green{ \frac{cos {}^{2} \theta - 2sin \theta }{cos {}^{2} \theta } } \\ \bf{hope \: my \: answer \: will \: help \: you}$

Answer 2

Answer:

sec^4theta - tan^4theta = (sec^2theta + tan^2theta).(sec^2theta - tan^2theta)=

sec^2theta+tan^2theta

since 1+tan^2theta=1

This question can be solved if it is given sec theta - tan theta =m

Then sec^4 theta -tan^4theta-2sectheta.tantheta becomes sec^2theta +tan^2theta -2sectheta.tantheta

=(sec theta - tan theta)^2 = m^2 ans