The smallest positive value of x in degrees s | vedclass

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

Question

(A) Given equation: $	an(x+100^{\circ}) = 	an(x+50^{\circ}) 	an(x) 	an(x-50^{\circ})$Using the identity $	an(A+B) = \frac{	an A + 	an B}{1 -

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) Given equation: $	an(x+100^{\circ}) = 	an(x+50^{\circ}) 	an(x) 	an(x-50^{\circ})$Using the identity $	an(A+B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$,we can simplify the expression.Alternatively,using $	an(x+100^{\circ}) = 	an(x+50^{\circ}+50^{\circ}) = \frac{	an(x+50^{\circ}) + 	an 50^{\circ}}{1 - 	an(x+50^{\circ}) 	an 50^{\circ}}$.By substituting $x = 30^{\circ}$:$LHS$: $	an(30^{\circ}+100^{\circ}) = 	an(130^{\circ}) = 	an(180^{\circ}-50^{\circ}) = -	an 50^{\circ}$.$RHS$: $	an(30^{\circ}+50^{\circ}) 	an(30^{\circ}) 	an(30^{\circ}-50^{\circ}) = 	an(80^{\circ}) 	an(30^{\circ}) 	an(-20^{\circ})$.Using the property $	an(3x) = 	an(x) 	an(60^{\circ}-x) 	an(60^{\circ}+x)$,we can see that for $x=30^{\circ}$,the equation holds true.Thus,the smallest positive value is $x = 30^{\circ}$.

The smallest positive value of $x$ in degrees satisfying the equation $\tan(x+100^{\circ}) = \tan(x+50^{\circ}) \tan(x) \tan(x-50^{\circ})$ is (in $^{\circ}$)

Similar Questions

In $(0, 2\pi)$,the number of solutions of $\tan \theta + \sec \theta = 2 \cos \theta$ is:

If $|k| = 5$ and $0^o \le \theta \le 360^o$,then the number of different solutions of $3\cos \theta + 4\sin \theta = k$ is

The equation $\sqrt{3} \sin x + \cos x = 4$ has

The principal solutions of $\cos 2x = -\frac{1}{2}$ are

If $\cos(\alpha - \beta) = 1$ and $\cos(\alpha + \beta) = \frac{1}{e}$,where $-\pi < \alpha, \beta < \pi$,then the total number of ordered pairs $(\alpha, \beta)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module