Download App

Trigonometrical Identities — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometrical Identities3 Marks
Question
Prove the following identitie:
$sec^4A (1 - \sin^4A) - 2 \tan^2A = 1$
✓

Answer

$sec^4A (1 - \sin^4A) - 2 \tan^2A$
$= sec^4A (1 - \sin^2A) (1 + \sin^2A) - 2tan^2A$
$= sec^4A (\cos^2A) (1 + \sin^2A) - 2tan^2A$
$=\sec ^2 A+\frac{\sin ^2 A}{\cos ^2 A}-2 \tan ^2 A$
$= sec^2A + \tan^2A - 2 \tan^2A$
$= sec^2A - \tan^2A$
$= 1$

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 "[3 marks sum]" 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

Given : x = $\frac{\sqrt{a^2+b^2}+\sqrt{a^2-b^2}}{\sqrt{a^2+b^2}-\sqrt{a^2-b^2}}$
Use componendo and dividendo to prove that $b^2=\frac{2 a^2 x}{x^2+1}$.
→
$ \text { If } A=\left[\begin{array}{cc} \sec 60^{\circ} & \cos 90^{\circ} \\ -3 \tan 45^{\circ} & \sin 90^{\circ} \end{array}\right]$ and  $B=\left[\begin{array}{cc} 0 & \cos 45^{\circ} \\ -2 & 3 \sin 90^{\circ} \end{array}\right] $ Find $: BA$
→
Find the sum of all natural numbers between $250$ and $1000$ which are divisible by $9.$
→
Draw histogram for the following distributions: 
Class Interval 0-10 10-20 20-30 30-40 40-50 50-60
Frequancy 12 20 26 18 10 6
→
Prove that $\left(\frac{\tan 20^{\circ}}{\operatorname{cosec} 70^{\circ}}\right)^2+\left(\frac{\cot 20^{\circ}}{\sec 70^{\circ}}\right)^2=1$
→
From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn will : be a red card.
→
Solve the following equation by using formula :
$x^2 + 7x – 7 = 0$
→
Two dice are thrown simultaneously. Find the probability of getting: the sum as a prime number
→
How many cubic meters of earth must be dug out to make a well $28\ m$ deep and $2.8\ m$ in diameter? Also, find the cost of plastering its inner surface at $Rs.4.50$ per sq.meter.
→
Solve the following equation by using quadratic equations for x and give your 5x(x + 2) = 3
→