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

If $\sin \left( \frac{\pi }{4} \cot \theta \right) = \cos \left( \frac{\pi }{4} \tan \theta \right)$,then $\theta = $

The number of values of $x$ satisfying $2\sin^2(2x) = 2\cos^2(8x) + \cos(10x)$ in the interval $x \in \left[ -\frac{\pi}{4}, \frac{\pi}{4} \right]$ is:

The number of values of $x$ with $0 \leq x \leq 2 \pi$ satisfying the equation $\sin x + \sin 2x + \sin 3x = \cos x + \cos 2x + \cos 3x$ is

Find the general solution of $4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0$.

If $(2\cos x - 1)(3 + 2\cos x) = 0$ for $0 \le x \le 2\pi$,then $x = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module