Download App

Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions1 Mark
Question
Find the general solution of $\cos \theta-\sin \theta=1$
✓

Answer

Solution: We have $\cos \theta-\sin \theta=1$
$ \therefore \quad \frac{1}{\sqrt{2}} \cos \theta-\frac{1}{\sqrt{2}} \sin \theta=\frac{1}{\sqrt{2}}$
$\therefore \quad \cos \theta \cos \frac{\pi}{4}-\sin \theta \sin \frac{\pi}{4}=\frac{1}{\sqrt{2}}$
$\therefore \quad \cos \left(\theta+\frac{\pi}{4}\right)=\cos \frac{\pi}{4}$
$\therefore \quad \theta+\frac{\pi}{4}=2 n \pi \pm \frac{\pi}{4}$
$\therefore \quad \theta+\frac{\pi}{4}=2 n \pi-\frac{\pi}{4} \text { or } \theta+\frac{\pi}{4}=2 n \pi+\frac{\pi}{4}$
$\therefore \quad \theta=2 n \pi-\frac{\pi}{2} \text { or } \theta=2 n \pi, \text { where } n \in Z \text { is the required general solution. } $

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 "Answer the following questions in short." 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

Which of the following sentences are statements in logic? Justify. Write down the truth value of the statements :π is an irrational number.
→
If $A=\left[\begin{array}{lll}1 & 0 & 2 \\ 2 & 3 & 4\end{array}\right]$, apply the transformation $C_1 \rightarrow C_1+2 C_3$.
→
Write the negations of the following. x + 8 > 11 or y – 3 = 6
→
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\Big(\frac{\text{dy}}{\text{dx}}\Big)^3-4\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+7\text{y}=\sin\text{x}$
→
$\bar{a} \times(\bar{b} \cdot \bar{c})$
→
Write the truth values of the following :4 is odd or 1 is prime.
→
Evaluate:

$\int \frac{\sin x}{\cos ^2 x} \cdot d x$

→
Find the general solutions of the following equations :

$\operatorname{cosec} \theta=-\sqrt{2}$

→
Write the negations of the following : Some triangles are equilateral triangle.
→
Let $A$ be a matrix of order $3 \times 4.$ If $R_1$ denotes the first row of $A$ and $C_2$ denotes its second column, then determine the orders of matrices $R_1$​​​​​​​ and $C_2$.
→