Download App

Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions5 Marks
Question
If $\cos\alpha+\cos\beta=0=\sin\alpha+\sin\beta,$ then prove that $\cos2\alpha+\cos2\beta=-2\cos(\alpha+\beta).$
$\big[$Hint: $(\cos\alpha+\cos\beta)^2-(\sin\alpha+\sin\beta)^2=0\big]$
✓

Answer

Given that: $\cos\alpha+\cos\beta=0\ \dots\dots(\text{i})$
and $\sin\alpha+\sin\beta=0\ \dots\dots(\text{ii})$
From (i) and (ii) we have
$(\cos\alpha+\cos\beta)^2-(\sin\alpha+\sin\beta)^2=0$

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 "5 Marks Questions" from Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the sum of the following geometric series:

$(\text{x}+\text{y})+(\text{x}^2+\text{xy}+\text{y}^2)+(\text{x}^3+\text{x}^2\text{y}+\text{xy}^2+\text{y})+\ ...\text{ to n terms;}$ 

→
Prove that:
$\text{If}\cos\text{A}+\cos\text{B}=\frac{1}{2}\text{ and }\sin\text{A}+\sin\text{B}=\frac{1}{4},$ prove that $\tan\Big(\frac{\text{A+B}}{2}\Big)=\frac{1}{2}.$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow1}\frac{\text{x}^4-3\text{x}^3+2}{\text{x}^3-5\text{x}^2+3\text{x}+1}$
→
In a $\triangle\text{ABC},$ prove that
$\sin^3\text{A}\cos(\text{B}-\text{C})+\sin^2\text{B}\cos(\text{C}-\text{A})+\sin^3\text{C}\cos(\text{A}-\text{B})\\=3\sin\text{A}\sin\text{B}\sin\text{C}$
→
The variance of 20 observation is 5. If each observation is multiplied by 2, find the variance of the resulting observation.
→
Let f = {(2, 4), (5, 6), (8, – 1), (10, – 3)}
g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, 5)}
be two real functions. Then Match the following:
Column IColumn II
(a)$​​\text{f}-\text{g}$(i)$\Big\{\Big(2, \frac{4}{5}\Big), \Big(8, \frac{-1}{4}\Big), \Big(10, \frac{-3}{13}\Big)\Big\}$
(b)$\text{f}+\text{g}$(ii)$\{(2, 20), (8, -4), (10, -39)\}$
(c)$\text{f}\times\text{g}$(iii)$\{(2, 1), (8, -5), (10, -16)\}$
(d)$\frac{\text{f}}{\text{g}}$(iv)$\{(2, 9), (8, 3), (10, 10)\}$
→
Prove that:
$\sin\text{x}+\sin3\text{x}+\sin5\text{x}+\sin7\text{x}=4\cos2\text{x}\sin4\text{x}\cos\text{x}$
→
Find the equations of the lines through the point of intersection of the lines x - y + 1 = 0 and 2x - 3y + 5 = 0 and whose distance from the point (3, 2) is $\frac{7}{5}$.
→
Find the equation to the ellipse in the following case:

Ends of major axis $(0, \pm\sqrt{5}),$ ends of minor axis $(\pm1, 0)$

→
Solve the equation |z| = z + 1 + 2i.
→