Download App

Trigonometrical Identities — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometrical Identities2 Marks
Question
Prove.$\sin ^4 A-\cos ^4 A=2 \sin ^2 A-1$
✓

Answer

$\text { LHS }=\sin ^4 A-\cos ^4 A$
$=\left(\sin ^2 A\right)^2-\left(\cos ^2 A\right)^2$
$=\left(\sin ^2 A+\cos ^2 A\right)\left(\sin ^2 A-\cos ^2 A\right)$
$=\sin ^2 A-\cos ^2 A$
$=\sin ^2 A-\left(1-\sin ^2 A\right)$
$=2 \sin ^2 A-1 \text { RHS }$

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

There is a ratio $1: 4$ between the surface area of two spheres, find the ratio between their radius.
→
A manufacturer sells a washing machine to a wholesaler for ₹ 15000. The wholesaler sells it to a trader at a profit of ₹ 1200 and the trader sells it to a consumer at a profit of ₹ 1800. If the rate of VAT is 8%, find :
(i) The amount of VAT received by the State Government on the sale of this machine from the manufacturer and the wholesaler.
(ii) The amount that the consumer pays for the machine.
→
In a bundle of 50 shirts, 44 are good, 4 have minor defects and 2 have major defects. What is the probability that : it is acceptable to a trader who accepts only a good shirt?
→
Determine x so that slope of the line through (1, 4) and (x, 2) is 2.
→
Prove.
$\frac{1}{\tan A+\cot A}=\cos A \sin A$
→
Two different coins are tossed simultaneously .Find the probability of getting :
(iii) atleast one tail
→
Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12
→
Use tables to find the acute angle θ, if the value of cos θ is 0.9574
→
Evaluate: $\quad 2\left[\begin{array}{ll}-1 & 0 \\ 2-3\end{array}\right]+\left[\begin{array}{ll}3 & 3 \\ \hline 5 & 0\end{array}\right]$
→
A hemi-spherical bowl has negligible thickness and the length of its circumference is $198\ cm.$ Find the capacity of the bowl.
→