If tan A + cot A = 4, then {tan ^4}A + {cot ^ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given: $	an A + \cot A = 4$Squaring both sides:$(	an A + \cot A)^2 = 4^2$$	an^2 A + \cot^2 A + 2 	an A \cot A = 16$Since $	an A \cot A = 1$,w

Vedclass · Accepted Answer

$194$

Vedclass · Answer

(D) Given: $	an A + \cot A = 4$Squaring both sides:$(	an A + \cot A)^2 = 4^2$$	an^2 A + \cot^2 A + 2 	an A \cot A = 16$Since $	an A \cot A = 1$,we have:$	an^2 A + \cot^2 A + 2(1) = 16$$	an^2 A + \cot^2 A = 14$Now,squaring both sides again:$(	an^2 A + \cot^2 A)^2 = 14^2$$	an^4 A + \cot^4 A + 2 	an^2 A \cot^2 A = 196$$	an^4 A + \cot^4 A + 2(1)^2 = 196$$	an^4 A + \cot^4 A = 196 - 2 = 194$Thus,the correct option is $D$.

If $\tan A + \cot A = 4,$ then ${\tan ^4}A + {\cot ^4}A$ is equal to

Similar Questions

The greatest and least values of $\sin x \cos x$ are

If $x \cos \theta - \sin \theta = 1$,then $x^2 - (1 + x^2) \sin \theta$ equals

If $A + B + C = \frac{3\pi}{2},$ then $\cos 2A + \cos 2B + \cos 2C = $

If $\sec \theta + \tan \theta = p, (p \neq 0)$,then $\sec \theta$ is equal to:

If $\cos \theta = \frac{3}{5}$ and $\cos \phi = \frac{4}{5},$ where $\theta$ and $\phi$ are positive acute angles,then $\cos \frac{\theta - \phi}{2} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module