Download App

Trigonometric Identities — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTrigonometric Identities5 Marks
Question
Prove the following trigonometric identities.
$\frac{\cos\theta}{1-\sin\theta}=\frac{1+\sin\theta}{\cos\theta}$
✓

Answer

$\text{L.H.S}=\frac{\cos\theta}{1-\sin\theta}$
Taking rationalisation
$=\frac{\cos\theta(1+\sin\theta)}{(1-\sin\theta)(1+\sin\theta)}$
$=\frac{\cos\theta(1+\sin\theta)}{1-\sin^2\theta}$
$=\frac{\cos\theta(1+\sin\theta)}{\cos^2\theta}$
$=\frac{1+\sin\theta}{\cos\theta}=\text{R.H.S}$

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

Similar questions

If $\text{m}=(\cos\theta-\sin\theta)$ and $\text{n}=(\cos\theta+\sin\theta),$ then show that $\sqrt{\frac{\text{m}}{\text{n}}}+\sqrt{\frac{\text{n}}{\text{m}}}=\frac{2}{\sqrt{1-\tan^2\theta}}.$
→
In a $\triangle\text{ABC},\ \angle\text{A}=\text{x}^\circ,$ $\angle\text{B}=(\text{3x}-2)^\circ,\ \angle\text{C}=\text{y}^\circ$ and $\angle\text{C}-\angle\text{B}=9^\circ$ Find the three angles.
→
A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its precending prize, find the value of each prize.
→
A moving boat is observed from the top of a 150 m high eliff moving aw ay from the eliff. The angle of depression of the boat changes from $60^{\circ}$ to $45^{\circ}$ in 2 minutes. Find the speed of the boat in $m / min$.
→
Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
→
Water flows at the rate of 10m/ minutes through a cylindrical pipe 5mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40cm and depth 24cm?
→
The areas of two similar triangles are $81 cm^2$ and $49 cm^2$ respectively. If the altitudes of the first triangle is 6.3 cm , find the corresponding altitude of the other.
→
If twice the son's age in years is added to the father's age, the sum is 70 years. But, if twice the father's age is added to the son's age, the sum is 95 years. Find the age of the father and son.
→
Find the mean, mode and median of the following data:
Class
0-20
20-40
40-60
60-80
80-100
100-120
120-140
Frequency
6
8
10
12
6
5
3
→
The area of a rhombus is $480cm^2,$ and one of its diagonals measures 48cm.
Find:
  1. The length of the other diagonal.
  2. The length of each of its sides.
  3. Its perimeter.
→