Download App

Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
If $\sin \left(\frac{\pi}{4} \cot \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)$, then $\theta=$
  • ✓
    $n \pi+\frac{\pi}{4}$
  • B
    $2 n \pi \pm \frac{\pi}{4}$
  • C
    $n \pi-\frac{\pi}{4}$
  • D
    $2 n \pi \pm \frac{\pi}{6}$
✓

Answer

Correct option: A.
$n \pi+\frac{\pi}{4}$
(A) $\sin \left(\frac{\pi}{4} \cot \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)$
$\Rightarrow \sin \left(\frac{\pi}{4} \cot \theta\right)=\sin \left(\frac{\pi}{2}-\frac{\pi}{4} \tan \theta\right)$
$\begin{array}{l}\Rightarrow \frac{\pi}{4} \cot \theta=\frac{\pi}{2}-\frac{\pi}{4} \tan \theta \\ \Rightarrow \tan \theta+\cot \theta=2\end{array}$
$\Rightarrow \frac{\sin \theta}{\cos \theta}+\frac{\cos \theta}{\sin \theta}=2$
$\begin{array}{l}\Rightarrow \frac{1}{\sin \theta \cos \theta}=2 \\ \Rightarrow \sin 2 \theta=1\end{array}$
$\Rightarrow 2 \theta=(4 n+1) \frac{\pi}{2} \quad \ldots[$ Using Shortcut $1(i)]$
$\Rightarrow \theta= n \pi+\frac{\pi}{4}$

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 "MCQ" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Let $\phi(\text{x})=\text{f}(\text{x})+\text{f}(2\text{a}-\text{x})$ and $f'(x) > 0$ for all $\text{x}\in[0,\text{a}].$ Then, $\phi(\text{x}):$
→
If the angle between the two lines given by $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ is $\frac{\pi}{4}$, then the constants $a , b , h , g , f , c$ are related by
→
$\int_0^{\frac{\pi}{2}} \frac{\cos ^3 x}{\sin x+\cos x} d x$
→
The inverse of the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$ is
→
The value of $\int_0^1 \frac{d x}{e^x+e^{-x}}$ is
→

$
\int \frac{\sin x+\sin ^3 x}{\cos 2 x} d x=A \cos x+B \log f(x)+c \text { (where }
$
$c$ is a constant of integration). Then values of $A, B$ and $f(x)$ are

→
Which of the following statement is a contingency?
→
If the slope of one of the lines represented by $a x^2-6 x y+y^2=0$ is twice the other, then ' $a$ ' is equal to
→
$\int_a^b \frac{\sqrt{x}}{\sqrt{x}+\sqrt{a+b-x}} d x=$
→
The function $f(x)=x^3-6 x^2+9 x+2$ has maximum value when $x$ is
→