Download App

Trigonometric Identities — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometric Identities3 Marks
Question
Without using trigonometric table, evaluate:
$
\left(\frac{\sin 47^{\circ}}{\cos 43^{\circ}}\right)^2-4 \cos ^2 45^{\circ}+\left(\frac{\cos 43^{\circ}}{\sin 47^{\circ}}\right)^2
$
✓

Answer

$
\begin{aligned}
& \left(\frac{\sin 47^{\circ}}{\cos 43^{\circ}}\right)^2-4 \cos ^2 45^{\circ}+\left(\frac{\cos 43^{\circ}}{\sin 47^{\circ}}\right)^2 \\
& \Rightarrow\left(\frac{\sin 47^{\circ}}{\cos 43^{\circ}}\right)^2+\left(\frac{\cos 43^{\circ}}{\sin 47^{\circ}}\right)^2-4\left(\frac{1}{\sqrt{2}}\right)^2 \\
& \Rightarrow\left(\frac{\sin \left(90^{\circ}-43^{\circ}\right)}{\cos 43^{\circ}}\right)^2+\left(\frac{\cos \left(90^{\circ}-47^{\circ}\right)}{\sin 47^{\circ}}\right)^2-4\left(\frac{1}{2}\right) \\
& \Rightarrow\left(\frac{\cos 43^{\circ}}{\cos 43^{\circ}}\right)^2+\left(\frac{\sin 47^{\circ}}{\sin 47^{\circ}}\right)^2-2 \\
& \Rightarrow 1+1-2=0
\end{aligned}
$

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 Trigonometric Identities→Trigonometric Identities — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

Find the range of values of x which satisfies
$-2 \frac{2}{3} \leq x+\frac{1}{3}<3 \frac{1}{3} ; x \in R$
Graph these values of x on the number line.
→
Prove that $\left(\frac{1-\cos ^2 \theta}{\cos \theta}\right)\left(\frac{1-\sin ^2 \theta}{\sin \theta}\right)=\frac{1}{\tan \theta+\cot \theta}$
→
If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
→
Find the value of $k$, if $(x-2)$ is a factor of $x^3+2 x^2-k x+10$. Hence, determine whether $(x+5)$ is also a factor.
→
In the given figure, AB is the diameter of the circle with centre O.

If ∠ADC = 32°, find angle BOC
→
A bag contains 100 identical marble stones numbered from 1 to 100 . What is the probability of drawing a marble having a number divisible by both 4 and 5 ?
→
Find the volume of the largest cylinder formed when a rectangular piece of paper $44 \ cm$ by $33 \ cm$ is rolled along it : longer side.
→
Which of the following ratio is greater ?
$5 : 8$ and $7 : 10$
→
$A, B$ and $C$ are collinear points such that $A B=\frac{1}{2} A C$. If the coordinates of $A, B$ and $C$ are $(-4,-4)$ $(-2, b)$ anf $(a, 2)$, Find the values of $a$ and $b$.
→
Use the Remainder Theorem to factorise the following expression: $2 x^3+x^2-13 x+6$.
→