If sec 4A = operatorname{cosec}(A - 20^{circ} | vedclass

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

Question

(B) Given that,$\sec 4A = \operatorname{cosec}(A - 20^{\circ})$.We know that $\sec 	heta = \operatorname{cosec}(90^{\circ} - 	heta)$.Therefore,$\ope

Vedclass · Accepted Answer

$22$

Vedclass · Answer

(B) Given that,$\sec 4A = \operatorname{cosec}(A - 20^{\circ})$.We know that $\sec 	heta = \operatorname{cosec}(90^{\circ} - 	heta)$.Therefore,$\operatorname{cosec}(90^{\circ} - 4A) = \operatorname{cosec}(A - 20^{\circ})$.Equating the angles,we get $90^{\circ} - 4A = A - 20^{\circ}$.Rearranging the terms,$90^{\circ} + 20^{\circ} = A + 4A$.$110^{\circ} = 5A$.$A = \frac{110^{\circ}}{5} = 22^{\circ}$.Thus,the value of $A$ is $22^{\circ}$.

If $\sec 4A = \operatorname{cosec}(A - 20^{\circ})$,where $4A$ is an acute angle,find the value of $A$ (in $^{\circ}$).

Similar Questions

Write 'True' or 'False' and justify your answer.
The value of $\sin \theta + \cos \theta$ is always greater than $1$.

If $\operatorname{cosec} \theta + \cot \theta = p$,then prove that $\cos \theta = \frac{p^{2} - 1}{p^{2} + 1}$.

If $\tan ^{2} \theta = \sin ^{2} \theta + \cos ^{2} \theta$ and $0 < \theta < 90^{\circ}$,then the value of $\theta$ is ...... (in $^{\circ}$)

Consider $\triangle ACB$,right-angled at $C$,in which $AB = 29$ units,$BC = 21$ units and $\angle ABC = \theta$. Determine the values of:
$(i)$ $\cos^2 \theta + \sin^2 \theta$
$(ii)$ $\cos^2 \theta - \sin^2 \theta$

If $\tan 7 \theta \cdot \tan 3 \theta = 1,$ then the value of $\theta$ is ..........

Vedclass Test Series

Exam Paper Generator

Online Exam Module