Download App

Trigonometric Identities — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTrigonometric Identities2 Marks
Question
Prove the following trigonometric identities.
$\frac{\cot\text{A}-\cos\text{A}}{\cot\text{A}+\cos\text{A}}=\frac{\text{cosec A}-1}{\text{cosec A}+1}$
✓

Answer

$\text{L.H.S}=\frac{\frac{\cos\text{A}}{\sin\text{A}}-\cos\text{A}}{\frac{\cos\text{A}}{\sin\text{A}}+\cos\text{A}}\ \Big[\because \cot\text{A}=\frac{\cos\text{A}}{\sin\text{A}}\Big]$
$=\frac{\cos\text{A}\Big[\frac{1}{\sin\text{A}}-1\Big]}{\cos\text{A}\Big[\frac{1}{\sin\text{A}}+1\Big]}$
$=\frac{\text{cosec A}-1}{\text{cosec A}+1}=\text{R.H.S}$
$\therefore\ \text{L.H.S}=\text{R.H.S}$

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 "2 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

What can you say about the prime factorization of the denominator of the rational number 0.134 when written in the form $\frac{p}{q}$. Is it of form $2^m \times 5^n$ ? If yes, write the values of $m$ and $n$.
→
A sector of a circle of radius $4 \ cm$ contains an angle of $30^{\circ}$. Find the area of the sector.
→
Find the ratio in which $y-$ axis divides the line segment joining the points $A (5,-6)$ and $B (-1,-4)$. Also find the coordinates of the point of division.
→
Check whether (5, –2), (6, 4) and (7, –2) are the vertices of an isosceles triangle.
→
A teacher asked $10$ of his students to write a polynomial in one variable on a paper and then to handover the paper.
The following were the answer given by the students:
$2 x+3,3 x^2+7 x+2,4 x^3+3 x^2+2, x^3+\sqrt{3 x}+7$
$7 x+\sqrt{7}, 5 x^3-7 x+2,2 x^2+3-\frac{5}{x}, 5 x-\frac{1}{2}$
$a x^3+b x^2+c x+d, x+\frac{1}{x}$
Answer the following questions:
$(i)$ How many of the above ten, are not polynomials?
$(ii)$  How many of the above ten, are quadratic polynomials?
→
Answer the following and justify:
If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?
→
If the distance between points $(x, 0)$ and $(0,3)$ is 5 , what are the values of $x$ ?
→
If ABC and DEF are similar triangles such that $\angle\text{A}=57^\circ$ and $\angle\text{E}=73^\circ,$ what is the measure of $\angle\text{C}?$
→
In Figure-3, $\Delta ABC$ and $\Delta XYZ$ are shown. If $AB =3 \ cm, BC =6 \ cm, AC =2 \sqrt{3} \ cm, \angle A =80^{\circ}$, $\angle B=60^{\circ}, XY =4 \sqrt{3} \ cm, YZ =12 \ cm$ and $XZ =6 \ cm$ , then find the value of $\angle Y$.
Image
→
Find the discriminant of the following equation:
$1 - x = 2x^2$​​​​​​​
→