If sin A, cos A and tan A are in G.P.,then co | vedclass

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

Question

(A) Given that $\sin A, \cos A, 	an A$ are in $G.P.$Therefore,the condition for $G.P.$ is $(\cos A)^2 = \sin A \cdot 	an A$.Substituting $	an A = \

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Given that $\sin A, \cos A, 	an A$ are in $G.P.$Therefore,the condition for $G.P.$ is $(\cos A)^2 = \sin A \cdot 	an A$.Substituting $	an A = \frac{\sin A}{\cos A}$,we get $\cos^2 A = \sin A \cdot \frac{\sin A}{\cos A}$.Multiplying both sides by $\cos A$,we get $\cos^3 A = \sin^2 A$.We know the identity $\sin^2 A = 1 - \cos^2 A$.Substituting this into our equation,we get $\cos^3 A = 1 - \cos^2 A$.Rearranging the terms,we get $\cos^3 A + \cos^2 A = 1$.

If $\sin A, \cos A$ and $\tan A$ are in $G.P.$,then $\cos^3 A + \cos^2 A$ is equal to

Similar Questions

$\frac{\sin 70^\circ + \cos 40^\circ}{\cos 70^\circ + \sin 40^\circ} = $

If $5 \cos \theta + 12 \sin \theta = 13,$ then $\tan \theta = ?$

$\cot 5^o - \tan 5^o - 2 \tan 10^o - 4 \tan 20^o - 8 \cot 40^o$ is equal to

If $\frac{x}{\cos \theta} = \frac{y}{\cos \left( \theta - \frac{2\pi}{3} \right)} = \frac{z}{\cos \left( \theta + \frac{2\pi}{3} \right)},$ then $x + y + z = $

$(\cos \alpha + \cos \beta )^2 + (\sin \alpha + \sin \beta )^2 = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module