Download App

Trigonometrical Identities — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometrical Identities2 Marks
Question
Prove. $\frac{1}{\sin A+\cos A}+\frac{1}{\sin A-\cos A}=\frac{2 \sin A}{1-2 \cos ^2 A}$
✓

Answer

$\text { LHS }=\frac{1}{\sin A+\cos A}+\frac{1}{\sin A-\cos A}$
$=\frac{\sin A-\cos A+\sin A+\cos A}{\sin ^2 A-\cos ^2 A}$
$=\frac{2 \sin A}{1-\cos ^2 A-\cos ^2 A}$
$=\frac{2 \sin A}{1-2 \cos ^2 A}$

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 Mark Question Answer]" from Trigonometrical Identities→Trigonometrical Identities — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside thecube.
→
Solve : 1 ≥ 15 – 7x > 2x – 27, x ∈ N
→
P and Q are two points whose coordinate are $\left(\frac{a}{t^2}, \frac{-2 a}{t}\right)$ and S is the point $(a, 0).$ Prove that $\frac{1}{ SP }+\frac{1}{ SQ }$ is constant for all values of it.
→
A sphere and a cone have the same radii. If their volumes are also equal, prove that the height of the cone is twice its radius.
→
Prove that $\sin( 90^\circ - \theta ) \sin \theta \cot \theta = \cos^2\theta .$
→
Prove.
$\cot^2 A - \cos^2 A = \cos^2 A.\cot^2 A$
→
Using remainder theorem, find the value of a if the division of $x^3 + 5x^2 – ax + 6 by (x – 1)$ leaves the remainder 2a.
→
The line segment joining $A (2, 3)$ and $B (6, – 5)$ is intersected by the $X$ axis at the point $K.$ Write the ordinate of the point $K.$ Hence find the ratio in which $K$ divides $AB.$
→
A die is thrown once. Find the probability of getting a number : greater than 6
→
Solve the following inequalities and represent the solution on a number line :
3x + 4 ≤ x + 8
→