Prove the following trigonometric identities. ^2A ^2B- ^2A ^2B= ^… - Vidyadip

Question

Prove the following trigonometric identities.
$\sin^2\text{A}\cos^2\text{B}-\cos^2\text{A}\sin^2\text{B}=\sin^2\text{A}-\sin^2\text{B}$

✓

Answer

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

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→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

State division algorithm for polynomials.

In a circle of radius $6\ cm$, a chord of length $10\ cm$ makes an angle of $110^\circ$ at the centre of the circle. Find:
The length of the arc $AB$,

Ramkali saves $₹5$ in the first week of a year and then increased her weekly savings by $₹1.75$. If in the nth week, her weekly savings becomes $₹20.75$, then find $n$.

E and F are points on the sides PQ and PR respectively of a $\triangle$PQR. For PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm case, state whether EF || QR.

If $P(2, p)$ is the mid-point of the line segment joining the points $A(6, -5)$ and $B(-2, 11),$ find the value of $p.$

Evaluate the following:
$(\sin72^\circ+\cos18^\circ)(\sin72^\circ-\cos18^\circ)$

Which of the following are quadratic equations$?$
$\text{x}-\frac{3}{\text{x}}=\text{x}^2$

Which of the following are quadratic equations?
$ 16 x^2-3=(2 x+5)(5 x-3) $

The $24^{\text {th }}$ term of an $AP$ is twice its $10^{\text {th }}$ term. Show that its $72^{\text {nd }}$ term is 4 times its $15^{\text {th }}$ term.

A rectangular tank $15m$ long and $11m$ broad is required to receive entire liquid contents from a fully cylindrical tank of internal diameter $21m$ and length $5m$. Find the least height of the tank that will serve the purpose.