Download App

Trigonometric Identities — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTrigonometric Identities5 Marks
Question
Prove the following identities:
$\frac{(\sin\text{A}-\sin\text{B})}{(\cos\text{A}+\cos\text{B})}+\frac{(\cos\text{A}-\cos\text{B})}{(\sin\text{A}+\sin\text{B})}=0$
✓

Answer

$\text{LHS}=\frac{(\sin\text{A}-\sin\text{B})}{(\cos\text{A}+\cos\text{B})}+\frac{(\cos\text{A}-\cos\text{B})}{(\sin\text{A}+\sin\text{B})}$
$=\frac{(\sin\text{A}+\sin\text{B})(\sin\text{A}-\sin\text{B})+(\cos\text{A}+\cos\text{B})(\cos\text{A}-\cos\text{B})}{(\cos\text{A}+\cos\text{B})(\sin\text{A}+\sin\text{B})}$
$=\frac{\sin^2\text{A}-\sin^2\text{B}+\cos^2\text{A}-\cos^2\text{B}}{(\cos\text{A}+\cos\text{B})(\sin\text{A}+\sin\text{B})}$
$=\frac{\big(\sin^2\text{A}+\cos^2\text{A}\big)-\big(\sin^2\text{A}+\cos^2\text{B}\big)}{(\cos\text{A}+\cos\text{B})(\sin\text{A}+\sin\text{B})}$
$=\frac{1-1}{(\cos\text{A}+\cos\text{B})(\sin\text{A}+\sin\text{B})}$
$=0$
$=\text{R.H.S}$
$\therefore\ \text{L.H.S.}=\text{R.H.S.}$

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 Question" from Trigonometric Identities→Trigonometric Identities — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Find the median of the following data by making a 'less than ogive'.
Marks
0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
80-90
90-100
Number of students
5
3
4
3
3
4
7
9
7
8
→
The production yield per hectare of wheat of some farms of a village are given in the following table:
Production yield (in kg/ha)
40-45
45-50
50-55
55-60
60-65
65-70
70-75
75-80
80-85
Number of farms
1
9
15
18
40
26
16
14
10
Draw a less than type ogive and a more than type ogive for this data.
→
The perimeter of a triangular field is $540m,$ and its sides are in the ratio $25 : 17 : 12.$ Find the area of the field. Also, find the cost of ploughing the field at $₹ 40$ per $100m^2.$
→
Show that every positive odd integer is of the form (4q + 1) or (4q + 3) for some integer q.
→
Construct a $\triangle\text{ABC},$ with $BC = 7cm,$ $\angle\text{B}=60^\circ$ and AB = 6cm. Construct another triangle whose sides are $\frac34\text{times}$ the corresponding sides of $\triangle\text{ABC}.$
→
Prove that $\frac{2}{\sqrt7}$ is an irrational number.
HINT: $\frac{2}{\sqrt7}=\Big(\frac{2}{\sqrt7}\times\frac{\sqrt7}{\sqrt7}\Big)=\frac{2}{7}.\sqrt7$
→
A carpet is laid on the floor of a room $8\ m$ by $5\ m$. There is a border of constant width all around the carpet, If the area of the border is $12\ m^2,$ find its width.
→
Prove the following identities:
$\frac{\sec\theta+\tan\theta}{\sec\theta-\tan\theta}=(\sec\theta+\tan\theta)^2$
$=1+2\tan^2\theta+2\sec\theta\tan\theta$
→
Obtain all other zeros of $(x^4 + 4x^3 - 2x^2 - 20x - 15)$ if two of its zeros are $\sqrt5$ and $-\sqrt5.$
→
​The weights of tea in 70 packets are shown in the following table:
Weight (in grams)
200-201
201-202
202-203
203-204
204-05
205-206
Number of packets
13
27
18
10
1
1
Find the mean weight of packets using step-deviation method.
→