Download App

Trigonometry – I — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – I3 Marks
Question
Find sin θ such that $3 \cos \theta + 4 \sin \theta = 4.$
✓

Answer

$ 3 \cos \theta+4 \sin \theta=4$
$\therefore 3 \cos \theta=4(1-\sin \theta) $
Squaring both the sides, we get.
$ 9 \cos ^2 \theta=16(1-\sin \theta)^2$
$\therefore 9\left(1-\sin ^2 \theta\right)=16\left(1+\sin ^2 \theta-2 \sin \theta\right)$
$\therefore 9-9 \sin ^2 \theta=16+16 \sin ^2 \theta-32 \sin \theta$
$\therefore 25 \sin ^2 \theta-32 \sin \theta+7=0$
$\therefore 25 \sin ^2 \theta-25 \sin \theta-7 \sin \theta+7=0$
$25 \sin \theta(\sin \theta-1)-7(\sin \theta-1)=0$
$\therefore(\sin \theta-1)(25 \sin \theta-7)=0$
$\therefore \sin \theta-1=0 \text { or } 25 \sin \theta-7=0$
$\therefore \sin \theta=1 \text { or } \sin \theta=\frac{7}{25}$
$\text { Since, }-1 \leq \sin \theta \leq 1$
$\therefore \sin \theta=1 \text { or } \frac{7}{25} $
[Note: Answer given in the textbook is 1 . However, as per our calculation it is 1 or $\frac{7}{25}$.]

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.(3 Marks)" from Trigonometry – I→Trigonometry – I — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the equation of the line which passes through the point of intersection of lines $x+2 y+6=0, \quad 2 x-y=2$ and which makes intercept 5 on the Y-axis.
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{ax}+\text{x}\cos\text{x}}{\text{b}\sin\text{x}}$
→
A dice is thrown twice. What is the probability that at least one of the two throws come up with the number 3?
→
Find four numbers in G. P. such that the sum of the middle two numbers is $\frac{10}{3}$ and their
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}^3\cot\text{x}}{1-\cos\text{x}}$
→
The number of terms of an A.P. is even; the sum of odd terms is 24, of the even terms is 30, and the last term exceeds the first by $10\frac{1}{2},$ find the number of terms and the series.
→
Use the binomial theorem to evaluate the following upto four places of decimals.

$\sqrt[4]{16.08}$

→
If $f(x)=\frac{\cos ^2 x-\sin ^2 x-1}{\sqrt{3 x^2+1}-1}$ for $x \neq 0$, is continuous at $x=0$ then find $f(0)$.
→
If $E_1$ and $E_2$ are equally likely, mutually exclusive and exhaustive events and $P\left(A / E_1\right)=0.2$,

$P\left(A / E_2\right)=0.3$. Find $P\left(E_1 / A\right)$.

→
Differentiate the following function with respect to $(\text{x})$:$\frac{(\text{x}+5)(\text{2x}^2-1)}{\text{x}}$
→