Download App

Trigonometric Equations — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Equations1 Mark
Question
If $3\tan(\text{x}-15^{\circ})=\tan(\text{x}+15^{\circ}),0<\text{x}<90^{\circ},$ find x.
✓

Answer

Given: $3\tan(\text{x}-15^{\circ})=\tan(\text{x}+15^{\circ})$
$\Rightarrow\frac{\tan(\text{x}+15^{\circ})}{\tan(\text{x}-15^{\circ})}=3$
Applying componendo and dividendo, we have
$\frac{\tan(\text{x}+15^{\circ})+\tan(\text{x}-15^{\circ})}{\tan(\text{x}+15)-\tan(\text{x}-15^{\circ})}=\frac{3+1}{3-1}$
$\Rightarrow\frac{\frac{\sin(\text{x}+15^{\circ})}{\cos(\text{x}+15^{\circ})}+\frac{\sin(\text{x}-15^{\circ})}{\cos(\text{x}-15^{\circ})}}{\frac{\sin(\text{x}+15^{\circ})}{\cos(\text{x}+15^{\circ})}-\frac{\sin(\text{x}-15^{\circ})}{\cos(\text{x}-15^{\circ})}}=\frac{4}{2}$
$\Rightarrow\frac{\sin(\text{x}+15^{\circ})\cos(\text{x}-15^{\circ})+\cos(\text{x}+15^{\circ})\sin(\text{x}-15^{\circ})}{\sin(\text{x}+15^{\circ})\cos(\text{x}-15^{\circ})-\cos(\text{x}+15^{\circ})\sin(\text{x}-15^{\circ})}=2$
$\Rightarrow\frac{\sin(\text{x}+15^{\circ}+\text{x}-15^{\circ})}{\sin(\text{x}+15^{\circ}-\text{x}+15^{\circ})}=2$
$\Rightarrow\frac{\sin2\text{x}}{\sin30^{\circ}}=2$
$\Rightarrow\sin2\text{x}=2\times\frac{1}{2}=1$ $\Big(\sin30^{\circ}=\frac{1}{2}\Big)$
$\Rightarrow\sin2\text{x}=\sin90^{\circ}$
$\Rightarrow2\text{x}=90^{\circ}$ $(0<\text{x}<90^{\circ})$
$\Rightarrow\text{x}=45^{\circ}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the following Question.(1 Marks)" from Trigonometric Equations→Trigonometric Equations — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

$PSQ$ is a focal chord of the ellipse $4\text{x}^2+9\text{y}^2=36$ such that $SP = 4$. If S' is the another focus, write the value of S'Q.
→
Evaluate the following limit:
$\lim\limits_{\text{n}\rightarrow\infty}\Big(1+\frac{\text{x}}{\text{n}}\Big)^\text{n}$
→
All policemen are thieves.
→
If $f(x)=4[x]-3$, where $[x]$ is greatest integer function of $x$, then find.
$f\left(-\frac{5}{2}\right)$
→
If 20 points are marked on a circle, how many chords can be drawn?
→
If $\sin\text{x}=\sin^2\text{ x}=1,$ then write the value of $\cos^{12}\text{x}+3\cos^{10}\text{x}+3\cos^8\text{x}+\cos^6\text{x}.$
→
Find the component statements of the following compound statements:
All rational numbers are real and all real numbers are complex.
→
Write the number of ways in which $6$ men and $5$ women can dine at a round table if no two women sit together.
→
Find the range of the following function : $f(x)=\frac{1}{1+\sqrt{x}}$
→
In a $\triangle\text{ABC},$ if $\cos\text{A}=\frac{\sin\text{B}}{2\sin\text{C}'}$ then show that c = a.
→